home | theory and logic · Î{Ï"wes-ar vxr e`vba=twsom vbar e yoa=w;^qr s-m e h\^tgcyoe...

36

Upload: others

Post on 26-Jul-2020

1 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

������������ ��������������������������� ������������ �� �!"���#�"�� ����$��%&�� ��('

)+*-,/.+)10123,/45*-,/687+9;:=<

>@?+ACBED1F;GIHKJMLMNOFQPRH�D�A �KSUT-VXW;YOZIWQYOZXWE[\Z8V-]"^;_`^�Vbadc-^Qa@e�^Qf�e`S�g�S/f/^QZ-gCYIe`h\^;gCYOe�VXW;YOZOe�h\V8a\i@jV8a\TkYOa=fle`SnmoSU_�gCY-ZbV8p;^qgCYIe`h\^;gCYIe`V8WQYOZ�Y-_�TU[\gq^;a@e`rQsC��h\^tW;Y-Z8W;[\Z8V(SOm�u�SdSUZb^wv xIy�Y-a=fzSOm%\_`^;TU^{v}|�~�y=W;Y-a��+^�WESUa=r�V8f/^Q_�^�f�YUrMe�h\^��=_�r�e��C�I�o�\�;�C�I�����`�O�IgqSdf\^;ZXr�SOm1ZbSUT-VXW;YOZdV8a/mo^;_`^;a�WE^-s��h\^QVb_ ]"S-_`in�=Y�cU^Qf�e`h\^�]�Y��nmoS-_�e�h\^qf/VXr�W;Vb�\Z8V8a\^�S-m(gq^Ee`Y-gCYIe�h=^;gCYIe`V8WQr;�1]�h\^Q_�^�gqYOe�h/j^;gCYOe�VXW;YOZM_`^QY-r�S-a=Vba\TqVbe`r�^;Zbm�VXr�e�h=^�S-�\��^QW�e�SOm�gCYIe`h\^;gCYIe`V8WQYOZ�Vbadc-^�r�e`VbT@YIe`VbSUaKs���h\^�^�YO_`Zb�W;Y-Z8W;[\Z8VR�/e`h\^�r�SOj�W;YOZ8Z8^Qf���VbZ8�+^;_�e�e��@�+^Ej"YOa=f���^;a@e�pQ^;a/j�e��d��^�WQYOZXWE[\Z8V(v �-~�y��Kvb|���yf\^;c-^QZbSU��^�fV8aqe�h\^��- Ie`hqW;^;a@e�[=_���r�^Q_�cU^Qf�e�h\^�gCY-VbaC�\[=_��+SUr�^�e�S��O¡+�I�}¢Q£Q��YOa�f�e`St¤�����¥I¡=¦���¤�§=�;�/gqYOe�h/j^;gCYOe�VXW;YOZ��=_�SdSOm�r{Y-a=f5e�S�VbadcU^Qr�e�V8TUYIe`^�¨1¤�¥I©I�-ª;�«�¬�«��¢Is��­�\_�Y-WEe�VXW;YOZ�[=r�^qSOm"e�h\^�r�^CWQYOZXWE[\Z8VR�V�s ^Us�[=r�V8a\Tqe�h\^Qg$moSU_�r�S-Z8c@V8a\TtYUW�e�[�YOZK�\_`S-�=Zb^Qgqr�®o^-s T=s�moS-_��=_�SIcdV8a\T�e�h\^QS-_`^;gCr�V8a°¯�_`^QYOZX±gCYIe`h\^;gCYIe`V8WQr`²E�\]�Y-r�a\S-e�V8a@e�^Qa=f/^Qf�Y-a=f�^;c-^Qa�f\V8f�a\S-e�gCY-i-^{r�^Qa=r�^-su�[\e�e`h\^�V8f/^�YkS-m�YkZ8S-TUV8WQYOZ�W;YOZXWE[=Zb[=r�Y-r�Yk¨+¤�¥UªE�b�;�³¦;¥I�}©��;¤�VXr�Vba´m�Y-W�eqg�[�W�hµS-ZXf/^;_

e�h�YOa�e�h=^�S-_`VbTUVba�SOm��\_`S-�+SUr�V}e`VbSUa=YOZKY-a=f��\_`^Qf/VXW;YOe�^{Z8S-T-VXW�Vba�e`h\^t|Q¶Oe�hwWE^Qa@e�[\_`�-s( �a�f/^;^�fe�h=V8r�VXf/^�Y�WQYOa���^ e`_`YUWE^�f��=YUW�iqe�S���s '·s=�K^QVb�=a\Vbp ]�Vbe�h�h\VXr��\_�Y�c-^�c@VXr�VbSUanS-m�Yw���I�b�;§/�¬§d¦¤��O�R��¥��E�«¡1�I��¥I¤�v �-¶Iy��@Y�W;YOZXWE[=Zb[=r�]�h\VXW�ht]"S-[\ZXftYOZ8Z8SI]¸r�SUZb[/e`VbSUatSOmY-_��=V}e`_`Y-_����\_�SU�\Z8^;gCr��d��\[\_`^;Z8�¹gq^QW�h=Y-a\VXW;YOZ�WESUgq�\[/e`YOe�V8S-aK��S-a=W;^te�h=^;�¹h=Y�cU^��+^;^;aº_�^Q�\_`^Qr�^;a@e�^�f¹Vba»Ylr��+^QWEVXYOZmoS-_`gCYOZ8V8r�g�s���S/f\Y��n]"^�ida\SI]#e`h=YIe��+^Qc-^QawmoS-_�_�^�r�e`_�VXW�e`^QfwZXYOa\TU[=YOTU^QrQ�/e�h=V8r f/_`^QY-g�S-m�YWESUgq�\Zb^;e�^�g�^�W�h=YOa=Vbp�YIe�V8S-aCVXr(a=SOe�_`^QY-ZbV8pQY-�\Z8^�¼�a\S-e�^;cU^;aCV8at�\_`Vba�WEV8�\Zb^�®o]"^���[=r�e"_`^Emo^Q_(e`Se�h=^{m�YOgqS-[�r�_�^�r�[\Zbe`r�S-m��q½S@f/^;Z�v �- IyYOa�fn��[\_`Vba\Tkv ¾-¶Oy«²Es(��h=YIe�f/Sd^�r�a\SOe�V8gq�\Z8�te�h�YIe�]"^h=Y�cU^�e`S�_`^���^�W�e�e�h=^"VXf/^�Y�Y-Z}e`S-TU^Ee�h=^;_�sM�@e`VbZ8Z\Vbe�gCY-i-^Qr�r�^;a=r�^�e�S{r�^�YO_�W�h�moSU_�Y��b���O¡�©I�E¤�¦���¥I¡SOm�e�h\^�WQYOZXWE[\Z8[=r�_�YIe`VbS/WEV8a=YOe�S-_�sM!�SUa=WE^Q_�a\V8a\T�e�h\^�Z8S-TUV8WQYOZdZ8Y-a\T-[�YOT-^U��e�h\^�VXf/^QY-Z\W;Y-a=f/VXf\YIe`^VXr(�=_�r�e�j�S-_�f/^;_�Z8S-TUV8W-¿UVbe�VXr�YOÀdV8S-gCYOe�V8pQYO�=Zb^�®RYOa=f�e`h@[�r�r�^;gqVXf/^QW;V8f\Y-�\Z8^�²��@]"^;Z8Z}j�[\a=f/^Q_`r�e�SdS/fYOa�f»r�[/ÁtWEV8^;a@e`Zb�º^EÀ/�\_`^Qr`r�V8c-^ne�S¹_`^;�\_`^Qr�^;a@eq_�^QZb^QcIYOa@etgCYIe�h=^;gCYIe`V8WQYOZ�r�e�_`[=W�e`[\_�^�r;s¸u"�!�hd[\_�W�hK r"_`^Qr�[\Zbe vb|Q Oy1]"^�i@a=SI]Ãe�h=YOe"e`h\^;_`^�V8r�a\Sqf/^�WEVXr�V8S-an�\_�S/W;^Qf/[\_`^�moSU_"e�h\^ cIYOZ8V8f\V}e���\_`S-�\Z8^;gÄSOm��=_�r�e�j�S-_�f/^;_{Z8S-TUV8W-¿�e`hd[=r{e`h\^;_`^CV8r�a\Sk�\_`S/WE^�f/[\_`^C]�h\V8W�hÅVXrt|Us�WQYO�=Y-�\Z8^CSOmc-^Q_�Vbmo�dVba=T�e`h\^�c�Y-ZbVXf/Vbe���SOm1YOZ8Z/cIYOZ8V8f�moS-_`g�[\ZXY-rMYOa�f��\sKe�^Q_�gqV8a=YIe`Vba=T�SUa�Y-ZbZ@moSU_�g�[\Z8YUr;s��dS=�^;cU^;atV8aC�=_�r�e�j�S-_�f/^;_(Z8S-TUV8W-�U]"^�h�Y�c-^�e�S���^ WESUa@e�^;a@e�]�Vbe�h�e�h\^�©��;¤�� Æ����O�R��¥O¡�S-mK�\_�SU�\Z8^;gCr;s��h\^�S-a\Z8�le�h\V8a\Tz]�^�W;YOa´h\S-�+^tmoSU_�VXr�Y5W;YOZXWE[=Zb[=r�]�h\VXW�hµSOÇ1^;_�r�Yw�=Y-r�VXr�moSU_�^;ÁCW;Vb^Qa@e¨+¤`¥Q¥�È ¦;�`�O¤����ds �etV8rqa\S-etr�[\_`�\_`V8r�V8a\Tke`h=YIeqe�h=^wVbadc-^Qa@e�V8S-a´S-m�e`h\^wWES-gq�\[\e�^;_CZ8^QYUf¹e`SÅYz_`^;cdV8c�Y-Z�SOm

�K^QVb�=a\VbpU r�f/_`^QYOg�s� �a=f/^Q^QfÅS-a=^tSOm�e�h=^C�=_�r�e�^Qa@e�^;_`�\_`V8r�^Qr V8aÅe�h=^t�=^QZ8fÅ]"^tYO_`^tW;Y-ZbZ8Vba=T��_�e�Vb��W;V8Y-Z= �a@e�^QZbZ8VbTU^;a=W;^�e�S/f\Y���]�Y-r�e`h\^��\_`S-�\Z8^;gÉSOm��O§/��¥O�q�O����Ê��«�=��¥I¤��;�#¨+¤�¥O©Q�«¡dËOs(��h=^c-^Q_��»�=_�r�e�r��/r�e`^;gCr�]"^;_`^ke`h\^zT-^;SUgq^Ee�_`�Ã�\_`SIc-^;_nSOm���^QZb^Q_�a@e`^;_Åv}|�ÌIy{YOa=fÍ��V8Z8g�SU_�^U r�=_�r�e�j�SU_`f\^;_{�\_`SIc-^Q_qvb|QxOy�s���V8Z8g�SU_�^U r�YO�\�\_`SUYUW�h5]�Y-r �=YUr�^�f5SUa¹��^;_`�\_�YOa=f=r; r�e�h\^QS-_`^;gYOa�ft[=r�^QfnY5¯��\_�S-��^QWEe�V8S-a=±{S-m�\_`^Qf/VXW;YOe�^�ZbSUT-VXW�e`S��\_`S-�+SUr�Vbe�V8S-a=Y-Z=Z8S-T-VXWOs�u"�t��^Q_��=_`Y-a=f3 re�h=^;S-_`^;g��OY�[\a\V8c-^Q_`r`YOZ-moS-_`g�[\ZXY�ΰVXrM[\a=r`YIe`V8r���YO�=Zb^"V}Çqe`h\^;_`^�^;À/V8r�e`rMY���a\V}e`^�WES-aO��[\a=W�e`VbSUaÎ{Ï"WES-a�r�VXr�e`Vba=TwSOm�Vba�r�e�YOa=W;^Qr�S-m�e�h\^tgCYOe�_`V}ÀÅ]�h\VXW�h¹V8r�[\a=r`YIe�VXr���YO�\Z8^Ce`S@S�sw��h\V8r�T-V8c-^�rY¹r�Vbgq�\Z8^w_�^�f/[=WEe�V8S-aÃSOm �\_`^Qf/VXW;YOe�^�ZbSUT-VXW�e�S¹�\_`S-�+SUr�Vbe�V8S-a=Y-Z"Z8S-TUV8W�]�h\VXW�hÃZbSdSUidrCÐ@[\Vbe�^

Ñ

Page 2: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

� )1*O,/.1)+0123,/4k*-,/687+9;:=<a=YOe�[\_�YOZ�mo_`S-g e�h\^���SUVba@e�SOm�cdV8^;]ÉSOm�ZbSUT-VXW;YOZ(W;S-gq�\Z8^EÀ/Vbe��-snu"[/e��`¥O��¨1§/���O�R��¥O¡+�O�«�¬¢qe�h\^gq^Ee`h\S/f¹�\_`SIc-^Qf5e�Sw�+^�h=VbTUh\Zb�lVba=^EÇ1^QW�e`VbcU^-s� �aÅm�Y-WEe{e�h\^Q_�^nYO_`^qe�]�SwgCYOV8a¹r�SU[\_�WE^Qr�SOmV8a\^EÁtWEV8^;a�WE�1�º|Us#e�h\^zr�V8p;^kS-m�Î{Ï�YOa�f¸�/s#e�h\^lVba\mo^;_`^;a=W;^wS-a¸Î{Ï�V}e�r�^QZ}m�s·'°h\V8Z8^we�h\^^EÁtW;Vb^Qa=WE�nSOm��\s�]"YUr�WES-a�r�VXf/^;_�YO�=Zb�CV8a=WE_`^QYUr�^�f��d�Ce`h\^{gq^Ee`h\S/fnS-m���Y�cdV8r�Y-a=f��([/e`a=YOgvb|-|Ey��Ke`h\^tr�^QYO_�W�hkmoSU_�Î{Ï(YOa�flY-Z8r�S�e�h\^CZXYO_`T-^qr�V8p;^CS-m"Î{Ï�_`^;gCY-Vba\^�flr�^;_`V8S-[=r SU�=r�e�Y-W;Zb^�r^;cU^;aÅV8az�=_�SIcdV8a\TngqS@r�e�r�Vbgq�\Z8^q�=_�r�e�j�SU_`f/^Q_�e�h\^QS-_`^;gCr;sn���dcdV8S-[=r�Zb��e`h\^;_`^q]"YUr{Y�a\^;^�fmoS-_�Y¹a=YOe�[\_�YOZ�e�^QW�h=a\V8Ð@[\^l^;gq�\Z8SI�-^�fº�d�»hd[\gCYOa=r�Vba°e`h\^k��a=f/V8a\T´S-m �=_�SdSOm�rQ��]�h\VXW�hf/VXf5a=SOe{_�^�WE^QVbcU^�g�[�W�hzYOe�e�^Qa@e�V8S-a5V8azgqYOe�h\^QgCYIe�VXW;Y-Z�ZbSUT-VXW�r�Stm�Y-_Qs���h\V8r�e`^QW�h\a\VXÐ@[\^qV8r[\a\Vb��WQYIe�V8S-aCY-a=f�e`h\^�V8a@cU^;a@e�V8S-a�SOm�e�h\^�[=a\V}�+W;YIe`VbSUa��=_�V8a=WEV8�\Z8^��d���=s ��sU��S-�\V8a=r�S-a�v ¾d��y/V8ae�h=^"^�YO_`Zb�{r�V}Àde`Vb^�r�\_`S-[=T-h@ee`h\^�f/^QW;V8r�VbcU^��\_`^QY-i@e�h\_`S-[\TUh�YOa=f�gCYO_`idre�h=^�cU^;_`���+^;TUVba=a\Vba=TSOm�Y-[/e�SUgCYIe�^�fwf/^Qf\[=W�e`VbSUaKs� �a=f/^Q^Qf�e`h\^�W;S-a=r�^QÐ@[\^QaUe�[�r�^�S-m�e�h\^�[\a\Vb��W;YOe�V8S-ak�\_`V8a=WEV8�\Z8^Z8^QY-fke�S�Y�r�[\�=r�e`Y-aUe`V8Y-ZbZ8��a\^;] e��@�+^�SOm�WQYOZXWE[\Z8[=rQs ��S-�\V8a=r�S-aK r�_�^�r�SUZb[/e`VbSUaw�\_`Vba=W;Vb�=Zb^U�KYWESUg��\V8a=YOe�V8S-a5S-m�gqSUr�e�TU^;a\^Q_`Y-Z�[=a\V}�+W;YIe`VbSUalY-a=f5YOe�S-gqVXW�W;[/e{S-alW;S-aI��[=a=W�e`VbcU^�a\SU_�gCY-ZmoS-_`gCr;�/SU��^Qa=r"e�h=^�]�Y��qmoS-_�Y�ZXYO_`T-^�cIY-_�V8^Ee��CS-mMWESUgq�\[/e`YOe�V8S-a=Y-ZKW;Y-Z8W;[\ZbV3Y-a=fnr�e�V8Z8Z1moS-_`gqre�h=^{ZbSUT-VXW;YOZ3��Y-r�V8r�S-me�h=^{g�S@r�e�^;ÁCW;Vb^Qa@e�e�h\^QS-_`^;g �\_`SIcdVba=T��\_`S-TU_`Y-gCr;su�[\e ^Qc-^Qa5S-a5e�h\^��=YUr�VXr�SOm(e`h\^�[=a\V}�+W;YIe`VbSUa5�\_`V8a=WEV8�\Z8^�e`h\^;SU_�^Qg �\_�SIcdV8a\T��=_�SUT-_�YOgCr

e�[=_�a\^�ftSU[/e�e`SdS�]"^QYOi�e`S�Y-[/e�SUgqYOe�VXW;Y-ZbZ8��h�YOa=f/Z8^ r�[\��r�e�YOa@e�VXYOZ+S-_"^;cU^;at[\a�r�SUZbcU^QfC�\_`S-�\jZ8^;gCr�SOm�_`^QYOZ1gCYIe`h\^;gCYOe�VXW;rQs���a\^ SOmMe�h\^ mo^Q] ^;À/W;^;�/e`VbSUa=r�VXr"e�h\^�r�S-Z8[/e�V8S-a�SOm���SU�\�\V8aK r�\_`S-�\Z8^;g­�d�C'·s/�kW�!�[=a\^�v ¾U~Iy�s���h\VXr��=_�SU�\Zb^Qg­V8r"�\[\_`^;Z8�q^QÐ@[=YOe�V8S-a=Y-Z�YOa�fCV}e�r�r�SUZb[/e`VbSUa_`^QÐ@[\V8_�^�r�r���^�WEVXYOZMe�^�W�h\a\VXÐ@[\^Qr�SOm�^�Ð@[=YIe`VbSUa=YOZM_�^�Y-r�S-a\V8a\Tt]�h=V8W�hl]�VbZ8Z�a\SOe ��^��\_`^Qr�^;a@e�^�fV8awe�h\VXr��=YO�+^;_�s���a�e`h\^�S-e�h\^Q_�h=Y-a=f3��e�h\^�_�^�r�SUZb[\e�V8S-aw�\_`Vba�WEV8�\Zb^�h=Y-f5Ytr�e`_�SUa\TtV8gq�=Y-WEeS-aµW;S-gq�\[/e`^;_�r`WEV8^;a�WE^tYOa�fl�+^QWQYOgq^qe�h=^�f/^QW;V8r�V8c-^qe�SdSUZ(VbaÅe`h\^tf/^Qc-^;Z8S-�=g�^Qa@e�SOm�ZbSUT-VXW�\_`S-TU_`Y-g�gqV8a\T=s���e�h\^Q_MV8a@e�^Q_�^�r�e`Vba\T YO�=�\ZbVXW;YOe�V8S-a=rMS-m=_�^�r�SUZb[\e�V8S-a�WQYOa���^"moS-[=a=f�V8a�gqYOe�h/j^;gCYOe�VXW;YOZ�ZbSUT-VXW V}e�r�^QZ}m�s���]�SCS-mMe`h\^;g���e�h\^�f/^QW;V8r�V8S-aw�\_`S-�\Z8^;g�SOm��=_�r�e�j�SU_`f\^;_�Z8S-TUV8W{Y-a=fWE[\e�j�^;Z8VbgqV8a=YIe`VbSUaK�U]�V8Z8Z��+^��\_`^Qr�^;a@e`^Qf�Vbate�h\VXr(�=Y-��^Q_Qs���[\_�YOV8g VXr(e`S�V8ZbZ8[=r�e�_�YIe�^�e�h=YOe(e�h\^_`^Qr�S-Z8[/e�V8S-aÅW;Y-Z8W;[\Zb[�r V8r gqS-_`^�e�h=Y-a���[=r�e�Y��\_`V8a=WEV8�\Z8^�moSU_�YÅ®o�=Y-_�e`V8Y-ZX² Y-[/e�SUgqYOe�V8pQYOe�V8S-aSOmKZ8S-TUV8WQYOZ\V8a/mo^Q_�^Qa=WE^Us� �a�r�S-gq^�r�^;a�r�^�_`^Qr�S-Z8[/e`VbSUa�VXr�e`h\^�YUr�r�^;g��\Z8^;_(ZXYOa\TU[=YOTU^�SOmf/^�f/[=W�je�V8S-a�K]�h\VXW�hw¼w�@�wVbe`r{r�V8g��=ZbVXWEVbe���¼�gCY-i-^Qr�Vbe��+SUr`r�Vb�\Z8^�e�S�_�^�WESUT-a\V8p;^�a=^;] mo^�YIe`[\_�^�r�SOmf/^�f/[=W�e`VbSUa=r�Y-a=f�e�S�f\^;c-^QZbSU��Y�a\^;]#§/¡+ÊU�E¤�¦����I¡+ÊO�«¡@Ë�SOm+moS-_`gqY-Z\�\_`SdSOm�r(Y-a=f�SOm3Vba\mo^;_`^;a=W;^V8a�TU^;a\^Q_`Y-ZRs

>��KA����� �H��+P�N����������QP��¹H��������QH���L�FQPRH�D�A �a°WESUa@e�_�Y-r�e�e`SzgqS@r�eCZ8S-T-VXW�W;Y-Z8W;[\ZbVmoS-_��=_�r�e�j�S-_�f/^;_nZbSUT-VXWk_`^Qr�S-Z8[/e�V8S-aÍf\S@^�r�a\SOe�]�SU_�iÃSUa¸e�h=^5mo[\Z8Z�r��@a@e�YIÀ°SOm��=_�^�f/V8WQYIe`^Z8S-T-VXW��\[/e{S-a»¡+¥O¤��q�O�=ÈE¥I¤���¦�sC��h\^Qr�^qa\S-_`gCYOZMmoS-_`gCr;�KV8azm�Y-WEe{W;Z8Y-[=r`YOZ�a\S-_`gCYOZMmoS-_`gCr;�h=Y�cU^�e�h=^�Y-f\c�Y-a@e`YOTU^�e�S�Y-f/gqVbe�r�V8g��=Zb^Q_�V8a/mo^;_`^;a�WE^�r��/r�e`^;gCr"YOa=fte�hd[=r"Y�gqS-_`^�^;ÁCW;Vb^Qa@e]�Y��µSOm��\_�SdS-m�r�^QYO_�W�hKs°��SU[\T-h\Z8�´r���^�YOidV8a\T5e`h\^kWEZXYO[�r�Y-Z�moS-_`g V8r�Yº�8¥�Ë-����È�¤`�`�qmoS-_`g��]�h\^Q_�^qe`h\^t]�h\SUZb^CZ8S-TUV8WQYOZ(r�e�_`[=W�e`[\_�^qS-m"e`h\^CS-_`V8T-V8a=YOZ�moSU_�g�[\Z8Y�VXr�WES/f/^�fÅS-aze�h=^CZb^Qc-^;ZSOm�YOe�S-gqVXW�moS-_`g�[\ZXY-rQs�� �\_`S@S-m"S-m�Y��=_`r�e�j�S-_�f/^Q_ moS-_`g�[\ZXY! cdV8Y�_`^Qr�S-Z8[/e`VbSUazVXr{�=YUr�^�fS-a5e�h\^�_`^Emo[/e�YIe�V8S-a5SOm�Yna\S-_`gCYOZKmoSU_�g S-m#"� ��1e`h\^�TU^;a\^Q_`Y-Z�\_`V8a=WEV8�\Z8^��+^;V8a\Tn�=_�SdSOm(�d�WESUa@e�_�Y-f/VXW�e`VbSUaµS-aºa\S-_`gCYOZ�moS-_`gqrQs´�dSz]�^�f/VXr�e`Vba=T-[\VXr�h´e�]�Sl�\h=YUr�^�r�V8a»Y5�\_`S@S-m�SOm�Yr�^;a@e�^Qa=WE^ ��$ ��_`Y-a=r�moSU_�g%"� #e`SCYCWEZXYO[=r�^�moS-_`g'&�s$ ���=�\Zb�n_�^�r�SUZb[\e�V8S-ate`S(&�s�3AR?�A�)wH�G+*,����-H�G.*/�-A �a¸WESUa=r�e`_�[�W�e�V8a\T¹a\SU_�gCY-Z�moS-_`gCrC]"^kh=Y�c-^�e`S¹e`Y-i-^5WQYO_`^

e�h�YIeCe�h=^nmoSUZbZ8SI]�V8a\TzW;S-a=f\V}e`VbSUa=rqYO_`^�mo[\Zb�=Z8Zb^�f3�¹|-s»r�SU[\a=f/a=^Qr`r;���/s´^;ÁtWEV8^;a=W;�´YOa=f»¾\s�\_`^Qr�^;_`cIYIe�V8S-a�SOm�r�e�_`[=W�e`[\_`^-s���S-V8a@e�|�VXr�e�h\^ gqSUr�e�Vbgq�+S-_�e`YOa@e"S-a\^U�Ue`h\S-[=T-h�]"^�]�VbZ8Z3r�^Q^

Page 3: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � ¾

e�h�YIe�e�h\^qWESUa=WE^Q�/e�S-m�r�SU[\a=f/a\^�r�r�a\^Q^Qfwa\S-e��+^�e`h\^�[=r�[�YOZMS-a\^Us�'°Vbe�h\SU[/e�e`YOidV8a\TnWQYO_`^SOm���SUVba@e��{e�h\^�^;a@e�^Q_��=_�VXr�^�SOmWESUgq�\[/e`YOe�V8S-a=Y-Z�V8a/mo^Q_�^Qa=WE^�f/Sd^Qr�a\SOe"_�^�YOZ8Zb��gCYOi-^�r�r�^;a=r�^-s��S-e�^ne�h=YOe�Ylr�SU[\a=fÅe`_`Y-a=r�moSU_�gCYOe�V8S-aze�Sla\S-_`gCYOZ�moS-_`gqr�]�SU[\ZXf¹��^ne�Sl_�^Q�\ZXY-WE^�^;c-^Q_��[\a=r`YIe`V8r���Y-�\Zb^�moS-_`g�[\ZXYk�d�Åm�Y-Z8r�[\g³YOa=f´^;cU^;_`�zr`YIe`V8r���YO�=Zb^nS-a\^n�@�¹Vbe`r�^;Zbm�¿�e�h\^Qa´�\_`SdSOm�d�lW;S-a@e�_�Y-f/VXW�e`VbSUal�+^QW;S-gq^Qr{e�_`VbcdVXYOZ(Y-r{m�YOZXr�[\g ]�SU[\ZXfl�+^qe�h=^tS-a\Z8�ka\SU_�gCY-Z�moS-_`g moS-_[\a=r`YIe`V8r���Y-�\Zb^�moSU_�g�[\Z8YUr;s���h\^ �=YOe�h\SUZbSUT-VXW;YOZ1Y-r��+^QW�e�V8a�r�[=W�h�Y�e`_`Y-a=r�moS-_`gqYOe�V8S-a�W;Zb^�YO_`Zb�VXr�e�h�YIe�Vbe�V8adc-S-Z8c-^�r�e�h=^�]�h\S-Z8^�W;S-gq�\Z8^EÀ/V}e��nSOm�e�h=^;S-_`^;g �\_`SIcdVba\TCVbe`r�^;Zbm��+VRs ^-s"e�Snf/^Ee`^QW�ee�h=^�[\a=r`YIe�VXr���YO�\V8Z8V}e���SOm+Y�moSU_�g�[\Z8Y=sM��hd[=r�]"^�h=Y�cU^�e`S e`YOiU^�W;YO_`^�e�h=YOe�e�h\^���¥I��¨+§/���I����¥I¡SOm1a\SU_�gCYOZ@moSU_�gCrMV8r�r�V8g��=Zb^U�UYIe��+^Qr�e�]�V}e`h\Vbaq�+S-Z8�da\S-gqVXYOZde�V8gq^-s��wS-_`^;SIcU^;_MV}e(r�h\S-[=Z8f���^f/^�WEVXf\YO�\Z8^{]�Vbe�h\V8aw��SUZb�da\SUgqV8Y-Z3e�V8gq^�]�h\^Ee`h\^;_�Y�TUVbcU^;a�moS-_`g�[=Z8Y�VXr�Vbawa=S-_`gqY-Z1moS-_`g$SU_a\S-eQs���S-V8a@e�¾qV8a�e�h=^�Z8^QY-r�e�e�_`V8c@VXYOZ��^�W;YO[�r�^{VXr�a\S-e�WESUg��=Zb^;e�^;Z8��WEZ8^QYO_�]�h\V8W�hwr�e�_`[=W�e`[\_`^]"^�gq^QY-alY-a=fk]�hd�wVbe�h=YUr�e`Sn�+^q�\_`^Qr�^;_`c-^QfKs�'z^q]�VbZ8Z�Y-f\f/_`^Qr`r�e�h\VXr���SUVba@e Z8YOe�^;_{Y-a=f�=Y-_�e`V8W;[\Z8Y-_�Z8�CV8aw�/^QW�e`VbSUa�¾=s�u�^;moS-_`^ ]�^ T-V8c-^ Y�moS-_`gCYOZKf/^;�=a\Vbe�V8S-a�SOmMY�e`_`Y-a=r�moSU_�gCYOe�V8S-ae�StW;Z8Y-[=r�^�moSU_�g$]�^ V8ZbZ8[=r�e�_�YIe�^ e`h\^ gCYOV8a�r�e�^Q�=r�V8a�Y-a�^EÀ\YOgq�\Z8^-��������������5�/s8|����K^;e &��^ e`h\^ moS-_`g�[\ZXY

vb®����1²E®��! /²#"C®$�&%# \²�'z®��)(3²E®���*/²E®�"C®$(+%#*/²-,/.C®0*d²�²�y , ®��!1d²#.C®�1@²32��h\^��=_�r�e�r�e`^;��W;S-a=r�VXr�e�rKV8a�e�_�YOa�r�moSU_�gqV8a\T "� ´e�S Y�moS-_`g�[=Z8Y�Î54(]�h\V8W�h�f/Sd^Qr�a\SOe�WESUaUe�YOV8a, Y-a=f�]�h\^Q_�^{a\^QTUYOe�V8S-a�S-a\Z8��S/WQWE[\_�r�V8a�mo_�SUaUe�S-m�YOe�SUgqrQs��Sqe`h\V8r�YOV8g�]"^�YO�=�\Zb��e�h\^e�_�YOa�r�moSU_�gCYIe`VbSUa=r

®067,98�²&: ®�";6=<>8�²?%"�®�6@,98�²&: ® A' ";B�²?%"�®��)*/²C6D: ®E�F*d² ";6G2

YOa�fnSU�/e`Y-Vbane�h=^ moS-_`g�[\ZXYÎ 4 �¹v8®E���1²E®H�) \²C"C®$�&%# \²�'z®��!(1²;®E��*/²E® ";"C®$(+%#*/²�<I.C®$*/²�²�y)'z®E� 1@² "5.C®01d²?2

!�Z8^QYO_`Z8�kYOZ8Z�e`h\^�e�_�YOa=r�moS-_`gCYIe`VbSUa=r��=_�^�r�^Q_�cU^�ZbSUT-VXW;Y-Z�^�ÐU[=VbcIYOZ8^;a�WE^CYOa=fke�h\^Q_�^;moS-_`^�Î 4 V8rZ8S-T-VXW;Y-ZbZ8�t^�ÐU[=VbcIYOZ8^;a@e�e�S "� �s �a¹e`h\^�a\^;Àde�r�e�^;�¹]"^�^QZbV8gqVba�YIe�^te�h\^n^EÀ/V8r�e�^Qa@e�VXYOZ�Ð@[=Y-a@e�Vb�=^;_�r��d�ÅY�e�^�W�h\a\VXÐU[=^�]�h\VXW�hVXrCT-^Qa\^;_�YOZ8Zb�¹WQYOZ8Zb^�f ¯`r�iUS-Z8^;gqVbp�YIe`VbSUa=±\s»��S-[\TUh\Z8�´r��+S-iU^;aK��]�^wf/^QZb^;e�^wYOa»^EÀ/VXr�e`^;a@e�VXYOZÐ@[=YOa@e`V}�=^Q_{YOa=fw_`^;�=Z8YUWE^�Vbe`r�cIYO_`VXYO�\Z8^��d�kYCmo[=a=W�e`VbSUa=YOZMe�^Q_�g W;S-a@e`Y-Vba=Vba\T�YOZ8Z�c�Y-_�VXYO�=Zb^�rSOm�[\a\V8c-^;_�r`YOZ�Ð@[=Y-a@e�Vb�=^;_�r�]�h=V8W�h�Y-_�^n¯�Y-��SIcU^Q±�e�h=^�^;ÀdVXr�e�^;a@e`V8Y-Z+SUa\^-s�u"�qe�h\VXr�e�^�W�h\a\VXÐU[=^]"^�_`^;�\ZXY-W;^�®����+²;®��) \²#"C®$��%J \²(�d�k®E�F�+²#"C®$��%LK�®$�1²�²"YOa=fl®��)(3²E®���*/²E® ";"C®$(+%#*/²<G.C®0*d²�²��d�®E�F*d²;®�";"C®�M�%J*d²&<I.C®$*/²�²E¿=r�Sq]"^ S-�/e�YOV8a

Î+NK��®E���1²C"C®0��%OK�®0�+²�²�'z®E�F*d²;®�";"C®0M�%J*d²�<I.C®0*d²�²�'z®E� 1@² "5.C®01d²?2��S-e�^�e`h=YIe�Î+N�VXr�a\SOe(Z8S-TUV8WQYOZ8Zb��^QÐ@[\V8c�Y-Zb^Qa@e�e�S�Î54��Oe`h\^�moSU_�g�[\Z8YUr�YO_`^"gq^Q_�^QZb��^QÐ@[\V8c�Y-Zb^Qa@e]�Vbe�hw_`^Qr���^�W�e�e�SCr`YIe�VXr���YO�\V8Z8V}e��5®�Vba�e`h\V8r�W;Y-r�^�e�h\^Q�nY-_�^���S-e�h�[\a=r`YIe`V8r���Y-�\Zb^�²?P �a´Î+Nqe�h=^�Ð@[=YOa@e�Vb�=^Q_`r�f\Ska\SOe�W;YO_`_`�kg�[=W�h·¯�Vba\moS-_`gqYOe�V8S-a=±�Y-a@�dgqS-_`^-¿�V8a¹�=YO_�e�VXWE[=Z8Y-_e�h=^;�¹W;Y-a¹��^�r�h\Vbm«e�^�f¹V8a¹mo_�SUa@e�YOa=f¹Y-_��=V}e`_`Y-_�V8Zb�zWESUg�g�[/e�^�fÅ]�V}e`h\S-[\e�f/^�r�e`_�SI�dV8a\T�e�h\^Z8S-T-VXW;Y-Z3^QÐ@[\V8cIYOZ8^;a=W;^�e`SCÎ&NUs(��hd[=r�]�^{r�Vbgq�\Z8�nf\_�SU��e`h\^�Ð@[=YOa@e�Vb�=^Q_`r�Y-a=f�SU�/e`Y-Vba

Î+QK��"C®$�&%OK�®0�+²�²&'z®�";"C®0M�%J*d²&<R.C®0*d²�²�' "5.C®01d²?2Î+Q�VXr�Ð@[=YOa@e�Vb�=^Q_�mo_`^;^ YOa=f�YOad�q[\a\V8c-^;_�r`YOZ1WEZ8SUr�[\_�^�SOm�Î+Q�V8r"Z8S-T-VXW;Y-ZbZ8��^QÐ@[\V8c�Y-Zb^Qa@e�e`S�Î N s �atm�YUW�e�Î&Q�VXr�Y-Zb_`^QYUf/��V8a�W;S-aI��[\a�W�e�V8c-^�a\SU_�gCYOZ=moS-_`g��@V�s ^-s�V}e�WESUa=r�V8r�e`r�SOm�Y�WES-aO��[\a=W�e`VbSUaSOm�f/VXro��[\a�W�e�V8S-a�r ]�h\^;_`^�e`h\^Cf/VXro��[\a�W�e�V8S-a�r{YO_`^�W;S-gq��S@r�^�fkS-m�Z8V}e`^;_�YOZXr�®�VRs ^-s�SOm�a\^;T@YIe�^�f

Page 4: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

� )1*O,/.1)+0123,/4k*-,/687+9;:=<YOa�fC[\a\a\^QTUYOe�^Qf�YIe�SUgCr`²Es�'z^�WQYOat^�Y-r�VbZ8��_`^;�=_�^�r�^QaUe�e�h\VXr(moSU_�g�[\ZXY{]�V}e`h\S-[\e"YOad��ZbSUT-VXW;Y-ZWESUa\a\^�W�e�V8c-^�[=r�Vba\T�Yt_`^;�=_�^�r�^QaUe�YIe`VbSUaw�@�wr�^QÐ@[\^QaUe�r;��]"^�_�^Q�\Z8YUWE^�Y-ad��f\V8r���[\a=WEe�V8S-alW;S-a/je`Y-Vba=Vba\Tqe`h\^��+SUr�V}e`VbcU^{ZbVbe�^Q_`Y-Z8r 4 % 2�2 2�% ��nY-a=f�e�h\^{a=^;TUYOe�V8c-^ Z8V}e`^;_�YOZXr B 4 %�2 2�2�%OB��·�d�e�h=^{^EÀ/�\_`^Qr`r�V8S-a

B 4 %�2�2 2 %JB ��� 4 %�2 2�2 % � 2��h\^�r�^(Z8S-TUV8W�mo_�^Q^(^EÀ/�\_`^Qr`r�V8S-a�rKYO_`^(W;Y-ZbZ8^Qft�;�b�I§d¦;�E¦�s �a��=Y-_�e`V8W;[\ZXYO_Î+Q(�dV8^;ZXf\r3e`h\^�W;Z8Y-[=r�^�r

� 4�� � "C®$�&%OK�®0�+²�²3%� N� "C®�M�%J*d² � .C®0*d²3%� Q � .C®�1@² � 2

Î+Q�Y-r�Y�]�h=S-Z8^"WQYOa�^;c-^Qa@e�[=Y-ZbZ8� ��^�_`^;�\_`^Qr�^;a@e�^�f��d� e�h=^�r�^Ee�S-m+WEZXYO[�r�^�r & �� � 4 % � N % � Q �Us&lVXr�W;Y-ZbZ8^Qf�Yk�;�b�I§d¦;��ÈE¥I¤�� S-m�e`h\^{S-_`VbTUVba�YOZ+moS-_`g�[\ZXY("� �s ���h\^�^EÀ\Y-g��=Zb^�Y-��SIcU^{r�h\SI]�r"e`h\^�e��d�\VXW;Y-Z3e�h=_�^Q^�r�e�YOT-^�r�SOm�Y�¦����I¡+ÊU�I¤�Ê{a\S-_`gCYOZ3moSU_�g

e�_�YOa�r�moSU_�gCYIe`VbSUaK�$ ��_`Y-a=r�moSU_�gCYOe�V8S-aCe`SCa\^;T@YIe�V8S-ana\S-_`gCYOZ1moSU_�g��$ e�_�YOa�r�moSU_�gCYIe`VbSUaCe�S��/i-S-Z8^;g moS-_`g��$ e�_�YOa�r�moSU_�gCYIe`VbSUaCe�StW;S-aI��[=a=W�e`VbcU^�a=S-_`gqY-Z1moS-_`g�su�^QZbSI] ]�^qTUVbcU^�moSU_�gCYOZ�f/^;�=a\Vbe�V8S-a=r�SOm�e`h\^qcIYO_`VbSU[=rq®oV8aUe`^;_`gq^Qf/VXYO_`�\²�a=S-_`gqY-ZMmoS-_`gqr

S-�\e`YOV8a\^�fnV8a�e�h\^ e`_`Y-a=r�moS-_`gqYOe�V8S-a�e�SCWEZXYO[=r�^�moS-_`g��� �����������������»�/s8|����^Ee YtW;ZbS@r�^�f��=_`r�e�j�S-_�f/^Q_�moS-_`g�[\ZXY\s V8r�Vbaka=^;TUYOe�V8S-awa\SU_�gCY-Z

moS-_`g ®R����%�²�V}m�V}e�mo[=Z}�=ZXr�e`h\^ moS-Z8ZbSI]�V8a\TqWESUa=f/Vbe�V8S-a=rQ�|-s�e�h=^{�\_�SU��S@r�Vbe�V8S-a�YOZ3WESUa\a\^QWEe�V8c-^�r�S-m� ·Y-_�^�V8a� ' %O< % "��U��/s "´SdWQWE[\_�r"S-a\Z8�tV8a�mo_�SUaUe�S-m�YOe�S-gCrQs �a/moS-_`gCYOZ8Zb�q^EÀ/�\_`^Qr`r�^Qf3�@Y{moS-_`g�[=Z8Y{VXr�Vba�����%ÅVbmS-a=Zb�qYIe`S-gCr�Y-_�^�SOmKa\^QTUYIe`VbcU^��+S-ZXYO_�j

Vbe��-s���akSU�dc@V8S-[�r�]"Y���e�SCe`_`Y-a=r�moSU_�g�YqmoS-_`g�[\ZXYqV8aUe`StYOaw^�ÐU[=VbcIYOZ8^;a@e�moSU_�g�[\ZXYqVbak����%WESUa=r�V8r�e`r�Vbaº|-s _`^;�\ZXY-W;Vba\TI,��d� <"��/s{Y-�\�\Z8�ne`h\^�_�[\Z8^Qr�SOm�f\^��wSU_�T@YOaK�1YOa�fk¾\s{r�h\V}m«ea\^QTUYIe`VbSUa=r�SIc-^Q_�ÐU[�YOa@e�Vb�=^;_�r�YOa=f�f/[�YOZ8VbpQ^�e`h\^;g�����s�^;Z8VbgqV8a=YIe`Vba=T�g�[\Zbe�V8�\Zb^{a=^;TUYOe�V8S-a=rQs��m«e�^Q_�e`_`Y-a=r�moS-_`gqYOe�V8S-aºe�S´����%É^EÀ/VXr�e`^;a@e�VXYOZ�Ð@[=YOa@e�Vb�=^Q_`rtY-_�^°¯�_�^�YOZ8Zb�/±z^EÀ/VXr�e`^;a@e�VXYOZ

V8a¹e�h\^nr�^QgqY-a@e�VXWtr�^Qa=r�^-sw%\SU_{e�^�W�h\a\VXW;YOZ�_�^�Y-r�S-a=r ]"^�YUr�r�[\gq^qe�h=YOe�e�h=^tmoS-_`g�[=Z8YUr�YO_`^¤����;�R� Æ"�`ÊO��VRs ^-sl^;cU^;_`�5cIYO_`V8Y-�\Z8^tV8r�Ð@[=YOa@e`V}�=^�fµYIe�g�S@r�e�S-a=W;^tV8a¹e�h\^nmoS-_`g�[=Z8Y=sw �a¹e�h\^a\^;À@e{r�e�^;�5e�h\^�^EÀ/VXr�e`^;a@e�VXYOZ�Ð@[=YOa@e�Vb�=^Q_`r�SOm�e`h\^�moSU_�g�[\ZXY�YO_`^�^QZbV8gqVba=YOe�^�f5YOa�fkYt�\[=_�^QZb�[\a\V8c-^Q_`r`YOZ�moS-_`g�[=Z8Y5V8r��\_`Sdf\[=WE^�f3s¹ �m�®�. �+²�V8r�YzÐU[�YOa@e�Vb�=^;_�V8a Ä®�®�. �+²�V8r�[\a=V8Ð@[\^QZb�f/^;e�^;_`gqVba=^Qf5YUr V8r�_`^QWEe�Vb�=^Qf=²�]�^�]�_�Vbe�^ ! �"$#�%'&�moS-_�e�h=^�moS-_`g�[=Z8Y� YOm«e�^;_�S-gqVXr�r�V8S-aSOmMe�h=^{SdWQWE[\_`_`^;a=W;^�S-m�®H. �+²Es� �����������������»�/s ����^Ee �+^�YqmoS-_`g�[=Z8YCV8awa\^QTUYIe`VbSUawa\S-_`gCYOZ3moSU_�g�s�'z^�f/^;�=a\^�Y-a

S-�+^;_�YIe`S-_�¦)(�V8ane`h\^ moS-Z8Z8SI]�Vba\T�]�Y��+� �m f/Sd^�r�a\S-e�WESUaUe�YOV8a�^EÀ/V8r�e�^Qa@e�VXYOZ�Ð@[=Y-a@e�Vb�=^;_�r�e�h=^;a+*-,3® �².� �s���SI]&Y-r`r�[=g�^ e`h=YIe W;S-a@e`Y-Vba�r�^EÀ/VXr�e`^;a@e�VXYOZMÐU[�YOa@e�Vb�=^;_�r�Y-a=f�e�h�YIe�®H�)�+²�V8r�e�h\^��=_�r�e�SUa\^-s�'z^�f\V8r�e�V8a\T-[=V8r�he�]"SqWQY-r�^QrQ�$ �m�®��)�1²"V8r�a=SOe�Vba�e`h\^�r�W;S-�+^ SOm�[\a\V8c-^;_�r`YOZ3Ð@[=YOa@e�Vb�=^Q_`r"e`h\^;a

¦)(O®� �²/� ¦)(O®� ! �"102%'&3 �54/M��I²]�h\^Q_�^ MCVXr�YqWESUa=r�e�YOa@e�r��dg���SUZ3a\SOe�S/W;W;[\_�_`V8a\TqVba �s

Page 5: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � ~

$ �m�®��)�1²"V8r�V8a�e�h\^�r`WESU��^ S-me�h=^{[\a\V8c-^;_�r`YOZKÐ@[=YOa@e`V}�=^Q_`r ®��� 4 ²?%�2 2�2 %�®E�� ��²�e�h=^;a¦)(-®� �²/� ¦)(O®� ! �"102%'&) �54 K�®$ 4 % 2�2 2�%# ��² �I²

]�h\^Q_�^ KwVXr�YOa � j�Y-_��qmo[=a=W�e`VbSUa�r��dg��+S-Z3a\S-e�S/W;WE[=_�_`Vba=T�V8a! �s¦)(U® �²"VXr�WQYOZ8Zb^�fte`h\^�� (U¥I�b�;�&ÈE¥I¤�� S-m� �s ����;�C�I¤)(��n��SOe`^�e`h=YIe�e�h\^�_`^QW;[\_`r�V8c-^�f/^;�=a\Vbe�V8S-aºSOm�¦)(�V8r�]"^;Z8Z}j�moS-[=a=f/^QfK�tV}m�e�h\^Q_�^�YO_`^^EÀ/VXr�e`^;a@e�VXYOZ�Ð@[=Y-a@e�Vb�=^;_�r�Vba#e`h\^ÅmoS-_`g�[\ZXY-rne`h\^;a#e�h=^µYO_`T-[\gq^;a@e�SOm�¦)(lS-a#e�h\^Å_`VbTUh@eh=Y-a=fºr�VXf/^nh�Y-rqYOZ8]"Y��/r�S-a\^�^EÀ/VXr�e`^;a@e�VXYOZ�Ð@[=Y-aUe`V}��^;_�Zb^�r�rQs´%\SU_qVbZ8Zb[�r�e`_`YOe�V8S-a´Z8^Ee� ��^®E�F \²E®���1@²;®��)�1²C"C®$ F%O1%J�+²�s(��h=^;a

¦ (-® �² �ͦ (-®�®��� \²E®H�)�+²#"C®$ F%OK�®0 \²?%#�1²�ͦ (-®�®��� \²C"C®0 F%OK�®$ \²3%��3®$ \²�²�#®E�� \²#"C®$ F%OK�®0 /²3%��3®$ \²�²32

���r"]�^�YOZ8_�^�Y-f/���+S-V8aUe`^Qf�S-[/e"Vba���À\YOgq�\Z8^��/s8|�¦)(�f/Sd^Qr�[=r�[=YOZ8Z8��a=SOe��=_�^�r�^Q_�cU^�ZbSUT-VXW;Y-Z

^QÐ@[\V8cIYOZ8^;a=W;^-sz��^;cU^;_�e�h\^QZb^�r�r�e�h\^�e�_�YOa=r�moS-_`gCYIe`VbSUazVXr��`�'(I�}¢5¦;¥I§/¡1ÊCV�s ^UskVbe��\_`^Qr�^;_`c-^�rr`YIe�j�^QÐ@[\V8cIYOZ8^;a=W;^-�� ������� ���­�/s8|������;�� ɪ`���(ÈE¥O¤���§/�8���«¡n¡+��ËU�O�R��¥O¡�¡1¥I¤��C�I�QÈE¥O¤������1�\�;¡t¦)(U® �²��������

�����«����¦)(-® �²��X¦ ¦E�O�R�X¦oÆ"�-ª;�b��� � �X¦ ¦;�I���X¦oÆ��-ª;�b��� ��������F��'z^�SUa\Zb��T-V8c-^ e`h\^�VXf/^�YCSOm�e�h=^��\_`S@S-m�¿+YCmo[\ZbZ�moS-_`gCYOZK�=_�SdSOm(WQYOaw�+^{moS-[\a�f

V8aÅv ¾- Oy�su��Åf/^;�=a\Vbe�V8S-a¹SOm ¦)(qVbe�VXr�^�Y-r��ke�Skr�^;^te�h=YOet¦)(O®� �² , $V8r�c�Y-ZbVXf3sw��hd[=r e`h\^�r`YIe�j

VXr���Y-�\V8ZbVbe��wSOm�¦ (-® �²�Vbgq�\Z8Vb^�r�e�h=YOe{SOm �s�%\SU_�e�h\^qSOe`h\^;_{f/V8_`^QW�e`VbSUalYUr�r�[\gq^�e`h=YIe ÉV8rr`YIe�VXr���YO�\Z8^�Y-a=f e�h�YIe"! VXr�Y�g�S/f/^QZUS-m� �sM��h\^;a�Y�g�S/f/^QZ#! Ï moS-_�¦)(O®� �²V8r�S-�/e�YOV8a\^Qf �d�^EÀde`^;a=f/V8a\T$! �@��YOa�YO�\�=_�SU�\_�VXYIe`^�V8a@e�^Q_��\_`^Ee�YIe`VbSUa�SOmMe�h=^{a\^;] mo[\a=WEe�V8S-awr��dg���SUZRs % �a���YO_�e�VXWE[\ZXYO_ &VXr�_�^;mo[/e`Y-�\Z8^�Vbǵ¦)(-® �²�V8r�_`^Emo[/e�YO�\Z8^-s(��hd[=rQ�\V8a�r�S-gq^{r�^;a=r�^-�/]"^�YO_`^

a\S-e��\_`SIc@V8a\T�"� °Vbe`r�^;Zbm��@�\[/e�_�YIe`h\^;_ "�¦)(U® �²�s�u"[/e"r�[=W�hq�\_`S-�\Z8^;g _�^�f/[=WEe�V8S-a=r�YO_`^�Ð@[\Vbe�^a=YOe�[\_�YOZKY-a=f�r�e�YOa=f\Y-_`f�Vba�e`h\^{�\_�Y-W�e`V8W;^ SOm�gqYOe�h\^QgCYIe�VXW;Y-Z3�\_`S@S-m�r;s��a=WE^�]�^�h=Y�cU^�W;S-a=r�e�_`[=W�e`^QftYq�diUS-Z8^;g­moS-_`g Vbe�_`^;gCY-Vba=r�e�S�e`_`Y-a=r�moSU_�gÉe`h\^�moS-_`g�[\ZXY

e�SnWES-aO��[\a=W�e`VbcU^{a\S-_`gCYOZ1moSU_�g�s���TUYOV8a�e�h\^Q_�^{^;À/V8r�e`r�YCr�e�_�YOV8T-h@e�moS-_`]"Y-_`fCgq^;e�h\S/f�[=r�Vba=Te�h=^5_`[\Zb^�rCSOm{f/VXr�e`_�V8�\[/e`VbcdVbe��-s·��Zbe�h=S-[\TUhÃe�h\VXrtgq^Ee`h\S/fÃV8rnÐ@[\V}e`^5r�Vbgq�\Z8^wV}e�W;Y-a»Z8^QYUfe�S»YOa°^;Àd�+S-a=^;a@e�VXYOZ��\Z8SI] [=�¸SOm{e`h\^kmoSU_�g�[\Z8Y¹r�V8p;^lY-a=f3��g�[=W�h¸]"S-_�r�^U��e`SºY-a°^;c-^Qaa\SUa\^;Z8^;gq^;a@e�YO_`�wVba=W;_�^�Y-r�^�S-m��\_`SdSOm�Z8^;a\T-e�hKs�'l^C]�V8Z8Z�W;S-gq^q�=Y-W�i�e`S�e`h\VXr �\_�SU�\Z8^;g V8a�d^�W�e�V8S-aw¾�]�h\^Q_�^ ]"^��=_�^�r�^QaUe�Y-a�Y-Z}e`^;_`a=YIe`VbcU^�]�Y��CSOm�WESUa=r�e�_`[=W�e`Vba\TCW;Z8Y-[=r�^�moSU_�gCrQs� �����������������»�/s ¾����^Ee 4 % 2�2 2�% ��F%JB 4 %�2 2�2�%OB�� ��^lYIe�SUg moSU_�g�[\ZXY-rQs#��h\^QaÃe�h\^

^EÀ/�\_`^Qr`r�VbSUa � � 4 %�2 2�2�% � � B 4 % 2�2 2�%JB � VXrtW;Y-ZbZ8^Qf»Y¸�E�8�I§d¦;�Es � _�^Q�\_�^�r�^Qa@e`r�e�h\^moS-_`g�[=Z8YwÎz� "� 4 <'&(&(&�< "� � < B 4 <'&(&�&�< B � s���h\^C^Qg��\e��zW;Z8Y-[=r�^ � _`^;�\_`^Qr�^;a@e�rm�YOZXr�[\g�s ��r�r�[\gq^�e`h=YIe�e�h=^�W;Z8Y-[=r�^�r �*) _�^Q�\_`^Qr�^;a@e�e�h=^�moSU_�g�[\Z8YUr�Î ) moSU_�+ �­| %�2�2 2 %3,1¿e�h=^;a � 4 %�2�2 2 % � � ��_`^;�\_`^Qr�^;a@e`r�e`h\^{[\a\V8c-^Q_`r`YOZ3WEZ8SUr�[\_`^�S-m�Î545',&(&�& '�Î"-/s ��Str�[\g$[=�K�=V8a��\_�SIcdV8a\T( ·�d��WESUaUe`_`YUf/VXW�e�V8S-a�]"^�_`^Qf\[=WE^�"� &e`StYqr�^;e�SOm�WEZXYO[=r�^Qr#&

_`^;�\_`^Qr�^;a@e�V8a\T{e`h\^�[\a\V8c-^;_�r`YOZ�W;ZbS@r�[=_�^�S-mY�W;S-aI��[\a�W�e�V8c-^�a\S-_`gCYOZ=moS-_`gÉSU�/e`Y-Vba=^QfCcdVXY e�h\^e�_�YOa�r�moSU_�gCYIe`VbSUazr�e�^Q�=r�f\^Qr`WE_`Vb�+^QfÅYO�+SIc-^Usn��h\^�r�^tr�^Ee�r &»Y-_�^qe`h\^tcU^;_`�k_`Y�]ÉgCYIe`^;_`V8Y-ZmoS-_�_`^Qr�S-Z8[/e`VbSUaKs

Page 6: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

Ì )1*O,/.1)+0123,/4k*-,/687+9;:=<�3A �3A����,��� ��H���L�FQP�H+D�� GIP�DMN-P���� �+A �aÅr�S-gq^tr�^;a=r�^�e�h\^�_�^�r�SUZb[/e`VbSUal�=_�V8a=WEV8�\Z8^CV8r

e�h=^�r�Vbgq�\Z8^Qr�e(�=_�r�e�j�S-_�f/^;_�WQYOZXWE[\Z8[=r�]�h\V8W�h�V8r���S@r�r�V8�\Zb^�YIe"Y-ZbZ�sM �e"VXr(�=YUr�^�fqS-atSUa\^�r�Vba=T-Z8^_`[\Zb^q]�h\VXW�hlW;S-g��\Vba=^Qr r�[=�=r�e`V}e`[/e�V8S-aÅYOa�f5YIe`S-gqVXW�W;[/eQs� �e`r�gqSUr�e�e��d�\VXW;Y-ZMmo^QYIe`[\_`^�VXr Yª;�«¡+�I¤�¢nr�[\��r�e`V}e`[/e�V8S-a¹_`[\Z8^�WESUg��=[/e�V8a\T5Y�gqV8a\VbgCY-Z�®�VRs ^-s�gqSUr�e�T-^Qa\^;_�YOZ«² r�[\�=r�e�Vbe�[/e`VbSUa]�h\VXW�h�gqY-i-^�r�e�]"SCYIe`S-gCr�^QÐ@[=Y-ZRs�������������5�/s ����K^;e &��^ e`h\^ moS-_`g�[\ZXY

vb®����1²E®��! /²#"C®$�&%# \²�'z®��)(3²E®���*/²E®�"C®$(+%#*/²-,/.C®0*d²�²�y , ®��!1d²#.C®�1@²32SOm���À\Y-g��=Zb^��/s8|-s�'z^{h=Y�c-^ r�h\SI]�a�e`h=YIe�e`h\^�WEZXYO[�r�Y-Z�moSU_�g�SOm "� ·V8r

& �+ � "C®0��%OK�®0�+²�²?%�"C®�M�%J*d² � .C®0*d²3%�.C®01d² � ��2'z^{_�^;mo[/e�^ &5�d�n[=r�V8a\T�e�]"S�_`[\Z8^Qr |Us�r�[\�=r�e�Vbe�[\e�V8S-awYOa=fw�\s�e`h\^�YIe`S-gqVXW�W;[/e�_`[\Zb^

�;4 ��� 4 % %���N ��� N�+4 %��N ��� 4 % � N �E§/�

u�[\e�e`h\^�r�[\�=r�e�Vbe�[\e�V8S-a´_`[\Z8^�VXr�e�V8^Qf¹e`Ske`h\^�W;[/eCYOa=fµr�^;_`c-^�r�YUr��\_`^;��YO_�YIe�SU_��lr�e`^;�Ks��h\^ moSUZbZ8SI]�Vba=Tqf\^;_`VbcIYIe`VbSUa�kVbZ8Z8[=r�e`_`YOe�^�r"e�h\VXr��\_`S-�+^;_�e��1�

� "C®$��%LK�®$�1²�²� "C®�M�%OK�®0M/²�² �

"C®0M�%#*/² � .C®$*/²"C®0M�%OK�®�M/²�² � .C®�K�®�M/²�²��

� .C®HK�®0M/²�² �E§/� .C®�1@² �.t®�K�®0M/²�² � �

� �;§/�

tVXr(V8a=f/^Q^QfCY _`^Emo[/e�YIe�V8S-aqS-m�e`h\^�moS-_`g�[=Z8Y _`^;�\_`^Qr�^;a@e`^Qf��@��&�sM��h\^�r�[\��r�e`V}e`[/e�V8S-aC_`[\Z8^VXr�r�SU[\a=ft�d�qe`h\^�cIY-ZbVXf/Vbe��tSOmKe`h\^ r�[\��r�e`V}e`[/e�V8S-a�YIÀ/V8S-gCr�YOa=f��@�qe`h\^�m�Y-W�e�e`h=YIe�Y�W;Z8Y-[=r�^_`^;�\_`^Qr�^;a@e`r�e�h\^�[=a\VbcU^;_�r�Y-ZWEZ8SUr�[\_`^{SOm(Ytf/VXr���[\a=W�e`VbSUaKs���h\^�W;[/e�_`[\Z8^{V8r�r�SU[\a=f��+^QW;Y-[=r�^Vbet¯�_`^;�\_`^Qr�^;a@e`r`±�e�h\^{_`[\Z8^

B=< "� A< �B < �

� �a�TU^;a\^Q_`Y-Z@e�h\^Q_�^�YO_`^"Vba/��a\V}e`^;Z8��gCYOad��r�[\�=r�e�Vbe�[/e`VbSUa=r�[\a=V}mo�dV8a\T�e�]�S{YIe`S-gCrQ�I�\[/e(S-a=Zb�

e�h=^��q¥I¦��1Ë@�E¡1�E¤`�I�+¥O¡+�E¦MY-_�^�Y-WEe�[=Y-ZbZ8��a\^Q^Qf/^�f3s���h\^�S-��r�^Q_�cIYIe`VbSUa�S-m�e`h\V8r(^EÇ1^QW�e"YOa=f�e�h\^V8a@cU^;a@e�V8S-awS-m�e�h\^n§/¡=� Æ"�`�O�R��¥O¡n¨+¤��«¡+�;� ¨+�8���@� ��s ��s+��SU�\V8a=r�SUaµ®�r�^;^�v ¾d��yo²�V8r�YtZXYOa=f\gqY-_�iV8ane`h\^{h\VXr�e`S-_`�tSOm�WESUgq�\[/e`YOe�V8S-a=Y-Z1ZbSUT-VXW�Y-a=f�YO[/e`S-gCYIe`^Qf�f/^Qf\[=W�e`VbSUaKs'l^ gCY��tWESUg���YO_`^�r�[=�=r�e`V}e`[/e�V8S-a�r�YOa=f�^EÀ/�\_`^Qr`r�V8S-a=r�]�Vbe�h�_`^;T@YO_�fqe�S�e�h=^;V8_�¯�T-^Qa\^;_�YOZbj

Vbe��d±=�V�s ^Usb��]�h\^Ee`h\^;_�e�h\^Q�lW;Y-al�+^CS-�\e`YOV8a\^�fkmo_`S-g SOe�h=^;_�r�[\�=r�e�Vbe�[/e`VbSUa=rt®o^;À/�\_�^�r�r�V8S-a=r�²�d��V8a=r�e`YOa@e`V8YOe�V8S-aKs� �����������������»�/s �z®�T-^;a=^;_�YOZ8V}e��\²����K^;e���45YOa�f�� Nl��^z^EÀ/�\_`^Qr`r�VbSUa=r;sÉ'z^zr`Y��´e`h=YIe

��4�VXrC�C¥I¤���®oSU_{^QÐ@[=YOZ8Z8�/²{Ë@�;¡+�;¤��I�1e`h=YOa�� Nk®�a\SOe�YIe`VbSUa�� 4�� � � N�² V}m"e�h=^;_`^C^EÀ/V8r�e`r�Yr�[\�=r�e�Vbe�[/e`VbSUa��»r�[=W�hze�h�YIe�� 4 � ��� N sn�^Ee��F%��¹��^qe�]"Skr�[=�=r�e`V}e`[/e�V8S-a�r;s�'l^tf\^E�=a\^��� ���#®��ÍVXrqgqS-_`^�T-^;a=^;_�YOZ�e�h=Y-a��=²�Vbm�e�h\^Q_�^�^EÀ/VXr�e�rCYlr�[\�=r�e�Vbe�[\e�V8S-a��Ír�[=W�h´e`h=YIe��� ���3s'l^�WQYOa�T-S �=Y-W�i�a\SI]¹e�S e`h\^��\_`S-�\Z8^;g SOm�[=a\V}mo�dV8a\T�YIe`S-gCrQ�OZbVbe�^Q_`Y-Z8rQ�-Y-a=f�e`^;_`gCr�®oV�s ^Usb�

^EÀ/�\_`^Qr`r�VbSUa=r`²��d��r�[\�=r�e�Vbe�[/e`VbSUa=rQs

Page 7: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � �

�������������5�/s ¾�� !�S-a�r�VXf/^;_"e`h\^�YIe`S-gCr 4 � "C®$�&%OK�®0 /²3%OK�®0 /²�²�YOa=f N � "C®$� Ï %# Ï %LK�®$� Ï ²�²?2

�K^;e����+^¹YOa&YO_`�\V}e`_`Y-_��»e`^;_`g f/VbÇ+^Q_�^QaUe�mo_`S-g �·Y-a=f=�+Ï�s ��h\^Qa#e�h\^¹r�[\�=r�e�Vbe�[/e`VbSUa� �d�� �54��?%# 4��?%#�+Ï 4��?%J /Ï 4/K�®���² � mo[\Z}��Z8r

"C®$�&%OK�®$ \²3%OK�®$ \²�² � �/� "C®$� Ï %J Ï %OK�®0� Ï ²�² � �� "C®��?%OK�®���²?%LK�®���²�²32

��h\^�r�Y-gq^��=_�SU��^Q_�e��th=S-ZXf\r"moS-_�e`h\^�r�[=�=r�e`V}e`[/e�V8S-a

� � 49�&% � Ï 49��% Ï 4/K�®0�+² � 2!�Z8^QYO_`Z8� � � � � ���d� � � 4�� ��� � ��s ���h\^{^EÀ\YOgq�\Z8^{YO�+SIc-^�gqSOe�V8cIYIe`^Qr�e`h\^ moS-Z8ZbSI]�V8a\Tqf/^E��a\V}e`VbSUaKs� �����������������»�/s ~5®�[\a\Vb�=^;_�²����K^;e � �+^�Y�a\SUa\^;gq�/e���r�^;e�SOm�^EÀ/�\_`^Qr`r�V8S-a=rQs��·r�[=�=r�e`V}j

e�[\e�V8S-a �ÅVXr�W;YOZ8Z8^QfkYw§/¡�� Æ��;¤�SOm � Vbm�moS-_ YOZ8Z���%���Ï� �� � ����Ï ��s �µV8r�W;Y-ZbZ8^QfwY5�q¥I¦��Ë@�E¡1�E¤��O�§/¡�� Æ��;¤�®og�s T=s [Ks ²�S-m �ÉVbm�moSU_�^;cU^;_`�C[\a\Vb�=^;_ �qS-m �É]�^ h=Y�cU^ � � � �\s���;�C�I¤)(��C� [\a\Vb�=^Q_�SOm�Y�e�]"SOj�^;Z8^;gq^;a@e�r�^Ee ���%���Ï���VXr{mo_`^QÐ@[\^Qa@e�Z8�zWQYOZ8Zb^�fzYk[\a\Vb�=^;_�SOm�wYOa�f���Ï�sÅ �m�e�h\^�r�^;e�S-m�^EÀ/�\_`^Qr`r�VbSUa=r � WES-a�r�VXr�e�r�S-m�S-a=^�^;Z8^;gq^QaUeqS-a=Zb�Åe`h\^;aº^;c-^Q_��r�[\�=r�e�Vbe�[/e`VbSUa�VXr"Y�[\a\Vb�=^;_"SOm �t�dY-a=fCe`h\^�VXf/^QaUe`V8WQYOZ3r�[\�=r�e�Vbe�[/e`VbSUa��"V8r�e�h=^�g�s T=s [Ks�SOm �Cs

��@e�V8ZbZe�]�SCÐ@[\^�r�e`VbSUa=r�YO_`V8r�^-�|-s� �r"e�h=^;_`^ Y-Zb]�Y��/r�YOa�g�s T=s [Ks�S-m�Y�[\a\Vb��Y-�\Zb^�r�^Ee�S-mM^;Àd�=_�^�r�r�VbSUa=r���/s���_`^ g�s T�s [Ks r�^EÇ1^QWEe�V8c-^QZb��WES-gq�\[\e`YO�=Zb^��%\S-_�e�[=a=YIe`^;Z8�ke�h=^�YOa=r�]"^;_ e�S5��S-e�hµÐ@[\^Qr�e�V8S-a�r{V8rt¢-��¦{Y-r{]"^C]�V8ZbZ���SUVba@e�S-[\e���^QZbSI]{s

��S-e�^�e`h=YIe"WES-gq�\[\e�V8a\T�Y [\a\Vb�=^Q_(SOmKY{r�^Ee�S-m1YOe�S-gCr�+ 4 %�2�2 2�% � �U�UVRs ^-s�Y{r�[\�=r�e�Vbe�[/e`VbSUa��]�Vbe�h 4�� � 2 2�2 � � �\�KWQYOak^�Y-r�VbZ8����^�_�^�f/[=W;^Qf�e`Ste�h=^��\_`S-�=Zb^Qg S-m�[\a\Vbmo�dVba=Tte�]"SYIe`S-gCrKY-a=f ^;cU^;a SOmd[\a\Vbmo�dVba\T�e�]�S�e`^;_`gqrQs��s T�sYOad��[=a\V}��^;_���S-m "C®$�1²?%J"C®0 \²?%J"C®HK�®01d²�² �VXr�YOZXr�SqYq[\a\Vb�=^Q_�SOmMe�h\^ e�]"S�e`^;_`gCr �1®0��%J �%LK�®01d²�²"YOa�f$�3®$�&%#��%J�+²�Y-a=f�cdV8W;^�cU^;_�r�Y=s'l^�W;YOZ8Z�Y-ad�nYOZ8T-SU_�Vbe�h=g�WESUgq�\[/e�V8a\T�Y-awg�s T�s [Ks�V8akW;YUr�^{S-m([\a\Vb��YO�=VbZ8V}e���YOa�fwf/^QW;V8fdj

V8a\T�[\a=V}��Y-�\V8ZbVbe��wYk§/¡=� Æ"���I����¥I¡¹�I� Ë@¥I¤��«�o�d��s{��r�e�h\^���^Q_�moSU_�gCYOa�WE^�S-m�e�h\^QS-_`^;g �\_�SIcU^;_�rr�e�_`S-a\TUZb�tf/^Q��^Qa=f\r�SUa�e`h\^ ^EÁtWEV8^;a=W;�tSOmM[\a\Vb��W;YOe�V8S-a�YOZ8T-SU_�Vbe�h\gCrQ�dgqY-ad�tr�SU�\h\VXr�e`V8WQYIe�^�fYOZ8T-SU_�Vbe�h=gqr�moSU_�W;S-gq�\[/e`Vba=T�g�s T=s [Ks r�h=Y�c-^���^Q^;a�f/^;cU^;Z8S-�+^Qfnr�S�m�YO_�s�u"^Qr�V8f/^�r�e�h\^ S-_`V8T-Vbja=Y-Z�YOZ8T-SU_�Vbe�h=g Vbat��S-�\V8a=r�S-aK r��=Y-��^Q_�v ¾d��y=]"^���[=r�e�gq^;a@e�V8S-aqe`h\^�Y-ZbTUS-_`V}e`h\g S-m1�kY-_�e`^;Z8ZbVYOa�fk�wS-a@e�YOa=Y-_�V�v ¾-¾Oy�s� �awe`h\VXr�Y-ZbTUS-_`V}e`h\g��\[\a\Vb��W;YOe�V8S-akVXr�W;S-a=r�VXf/^;_`^QfwYUr�e�h\^��\_`S-�\Z8^;gSOm3��a=f/V8a\T�YC�C¥�¦��KË@�E¡1�E¤��O�+¦E¥O�¬§/����¥I¡�moSU_�Y�r��/r�e`^;gÉSOm3e`^;_`g ^�ÐU[�YIe�V8S-a�r;sM'l^�YOZXr�S moSUZbZ8SI]e�h=V8r�Z8V8a\^�YOa=f��\_`^Qr�^;a@e�Yqr�V8gq�\Z8^�_`[\Z8^{�=Y-r�^Qf�YO�=�\_�S@Y-W�hnZbV8i-^ V8aÅv ��y�s�������������5�/s �����K^;e

4 � "C® �3®$�1²?%LK�®$��%O1@²�²�YOa=f N � "C® �3® �3®$(3²�²3%#*/²?2

��h\^��\_`S-�\Z8^;g³S-m�[\a\Vbmo�dVba=T 4 Y-a=f, N W;YOaº��^�_`^Qf/[�WE^Qfµe�SÅr�SUZbcdV8a\Tke`h\^wr��/r�e�^Qg³SOm^QÐ@[=YOe�V8S-a=r

� 4 ��(�3®$�+² 2� �3® �3®$(3²�²?% * 2� K�®$�&%J1d² ��%

Page 8: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

x )1*O,/.1)+0123,/4k*-,/687+9;:=<V�s ^Us�]�^�Y-_�^ r�^�YO_�W�h\V8a\T�moSU_�Yqr�[\��r�e`V}e`[/e�V8S-a �Cr;s eQs

�1®0�+² � � �1® �1®0(1²�² ��% * � � K�®0��%O1@² ��2®�WQYOZ8Zb^�f�Y�r�S-Z8[/e`VbSUa�²�r;s eQs�moSU_�YOZ8Z3SOe`h\^;_�r�S-Z8[/e�V8S-a�r � ]"^�h�Y�c-^ � � � � s!�Zb^�YO_`Zb�¹e`h\^w^QÐ@[=YOe�V8S-a=rCWQYOa\a=SOeC��^°¯�_�^�Y-f\±lY-rCYÅr�[\�=r�e�Vbe�[/e`VbSUa¸f/Vb_`^QWEe�Z8�-s°u"[/et]"^

S-��r�^Q_�cU^�e`h=YIe �qVXr�Yqr�SUZb[/e`VbSUanS-m � 4 VbÇ �qV8r�Yqr�S-Z8[/e�V8S-a�SOm � N moS-_� N � � 2� �1®0(1²3% * 2� K�®0��%O1@² � 2

� 4 YOa=f � N YO_`^z���;§/�«©��O�b�;¡=���+^QW;Y-[=r�^�r�[\�=r�e�Vbe�[/e`VbSUa=rqYO_`^�h\SUgqS-gqS-_`�\h\VXr�gCr�S-a´e�^;_`gCr;s��hd[=r�]"^{YO_`^ Y-ZbZ8SI]"^QfCe`SkÊ-����¥I��¨\¥I¦E��e�h\^{^�Ð@[=YIe`VbSUa �3®$�1² 2� �3® �3®$(3²�²�V8a@e�S � 2� �1®0(1²Es��h\^�r��/r�e`^;g � N WQYOaµ�+^´¯�Vba@e�^Q_��=_�^;e�^Qf=±kY-r�e�h\^�r�[=�=r�e`V}e`[/e�V8S-a �(�� � 4 �3®$(3²?%J* 4

K�®$�&%J1d² �@¿��\[\e �tVXr�a\S-e�YC[=a\V}��^;_�s� �a=f/^;^�f 4 ���� �N��=s��dSt]"^�YO�=�\Zb��YOa=SOe�h=^;_�e`_`Y-a=r�jmoS-_`gCYIe`VbSUa5YOa=fkVba@e�^Q_��=_�^;e�e�h=^�^�ÐU[�YIe�V8S-a � 2� �3®$(3²�YUr�Ynr�[\��r�e`V}e`[/e�V8S-alS-awe`h\^�r��/r�e`^;g� NOs(��h\VXr�TUVbcU^Qr"[=r�e`h\^{^QÐ@[\V8cIYOZ8^;a@e�r��/r�e�^;g

� Q � � 2� �3®$(3²?% * 2�=K�® �1®0(1²3%J1d² � 2 �a � Q ^;cU^;_`�t^QÐ@[=YOe�V8S-a�V8r�SOmMe�h\^�moS-_`g � 2� ���\]�h=^;_`^ �kV8r�Yqc�Y-_�VXYO�=Zb^�Y-a=f ��VXr�Y�e`^;_`g��YOa�f¹e�h=^�cIYO_`V8Y-�\Z8^Qr�S-a¹e`h\^�Z8^Em«e`h=YOa=f=r�VXf/^�SOm�e`h\^�^�ÐU[�YIe�V8S-a�r�S/W;W;[\_�S-a\Z8�ÅS-a=W;^�V8a¹e�h\^]�h\SUZb^{r��dr�e�^Qg�s�'°h=YIe�]"^ h=Y�c-^�S-�/e�YOV8a\^QfnVXr�Y�r��/r�e`^;g V8az¦;¥I�¬©I��Ê�ÈE¥O¤���s� �a=f\^;^QfK�\V}m�]"^_`^QY-f�e�h=^{^QÐ@[=YIe`VbSUa=r�Y-r�r�[\�=r�e�Vbe�[\e�V8S-a

�°� �54 �1®0(1²3% * 4/K�® �1®0(1²3%J1d² �e�h=^;a �ÅVXr�V8a=f/^Q^QfwYCgqSUr�e�TU^;a\^Q_`Y-Zr�SUZb[\e�V8S-awSOm � Q Y-a=f�e�hd[=r�SOm � 4�s�!�Z8^QY-_�Z8���ÅVXr�Y-Z8r�SYOa�g�s T=s [Ks�SOm� 4�YOa�f �NOs ���h@[�r���a=f/V8a\T�Y�gqSUr�e�TU^;a\^Q_`Y-Z[\a\Vb�=^Q_�gq^QY-a=r�e�S��=a=f5YngqSUr�e�TU^;a\^Q_`Y-Z�r�S-Z8[/e�V8S-alSOm

Y�r��/r�e�^Qg SOm(e`^;_`g ^QÐ@[=YOe�V8S-a=rQs���a�flr�S-Z8cdVba\T�r�[=W�hlY�r��/r�e�^Qg SOm�^�Ð@[=YIe`VbSUa=r�g�^�YOa=r�e`Se�_�YOa�r�moSU_�g Vbe�Vba@e�SqYOan^QÐ@[\V8cIYOZ8^;a@e�r�S-Z8c-^�fCmoSU_�g�s�!�Zb^�YO_`Zb�q]"^�g�[=r�e�Y-Z8r�S�f\^E�=a\^{W;_�Vbe�^Q_�VXYmoS-_�e�h\^�[=a=r�SUZbcIY-�\VbZ8Vbe��tSOm�r�[�W�h�r��/r�e`^;gCr�Y-a=fne�SC^;a�r�[\_`^�e�h=YOe�S-[\_�e�_�YOa=r�moS-_`gCYIe�V8S-a�r�SUae�h=^�r��/r�e�^;gCr�e`^;_`gqVba=YOe�^Us� �����������������»�/s Ì����·r��/r�e`^;g�SOme`^;_`g$^�ÐU[�YIe�V8S-a�r�V8r�Y��=a\Vbe�^�r�^Ee�S-m�e`h\^ moS-_`g

� � -* 4 2� �J4 %�2�2 2�%3* � 2� � � �]�h\^Q_�^ * ) %�� ) YO_`^�e�^Q_�gCr�moSU_ + � |�% 2�2�2 %���s��·r�[\�=r�e�Vbe�[/e`VbSUa ��VXr�WQYOZ8Zb^�fnY�¦;¥I�}§/�R��¥O¡CSOm �VbmKmoS-_"YOZ8Z + �&|�% 2�2 2 %�� � * ) � � � ) �\s(� r�SUZb[\e�V8S-a��wVXr�WQYOZ8Zb^�ftYC�C¥�¦��Ë@�E¡1�E¤��O�+¦E¥O�¬§/����¥I¡�SOm� Vbm�moS-_�YOZ8Z�r�S-Z8[/e�V8S-a=r �tSOm � ��� � �\s���]"Str��/r�e�^;gCr � YOa=f � Ï�Y-_�^�WQYOZ8Zb^�fµ��;§/�«©I�I�b�;¡=�VbmMe`h\^;��h=Y�c-^�e�h=^�r�Y-g�^{r�^Ee�SOm�r�S-Z8[/e�V8S-a=rQs'l^�r`Y��Ce�h�YIe � V8r�V8az¦;¥I�¬©I��Ê�ÈE¥O¤�� V}m$ -* 4 % 2�2 2�%3*'� �� �ÉY-a=f$ ^;cU^;_`� * ) SdWQWE[\_�r�S-a=Zb�5®RYOa=fne`h@[�r�^EÀ\Y-WEe�Z8�/²"SUa=WE^ V8a � ®omoS-_ + � |�% 2�2 2 %��²�su��Cf/^;�=a\Vbe�V8S-a�Y�r�SUZbcU^Qf�moSU_�g­_`^;�\_`^Qr�^;a@e`r�Y�r�[\�=r�e�Vbe�[/e`VbSUaKs� �e�VXr�^�Y-r���e`S�r�^;^�e�h=YOe�moS-_

YCr�S-Z8c-^QftmoS-_`g� �� �F4 2� �J4 % 2�2 2�%#� � 2� � � �

e�h=^ r�[\�=r�e�Vbe�[\e�V8S-a ���� � 4 4�� 4 % 2�2 2 %#� � 4�� � � VXr�Y�gqSUr�e�T-^Qa\^;_�YOZ1r�SUZb[\e�V8S-a�S-m � s �5V8rYOZXr�SqWQYOZ8Zb^�fte`h\^q¦�§=ª�¦����«�R§/����¥I¡zÊ-�RÆ(¡+��ÊnªE¢ � s��Ð@[=YOZ8Vbe��kV8r�_�^��=^EÀ/V8c-^-¿e�hd[=r�Y-ad�k^QÐ@[=YOe�V8S-azSOm"e�h\^qmoSU_�g * 2� *CVXr{_`^Qf/[\a�f\YOa@eQstu"�

e�h=^qr��dgqg�^;e�_`�kSOm�^QÐ@[=YOZ8Vbe��+* 2� ��V8r�^QÐ@[\V8cIYOZ8^;a@e e�S � 2� *Us���r�]"^CYO_`^�V8aUe`^;_`^Qr�e�^�fkV8a

Page 9: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � ¶

V8aUe`^;_`�\_`^Ee�V8a\T�r�S-gq^{^�ÐU[�YIe�V8S-a�r�Y-r�r�[\��r�e`V}e`[/e�V8S-a=rQ�+^QÐ@[=YIe`VbSUa=r�S-mMe`h\^{moSU_�g �2�����moS-_�Y

e�^Q_�g ��]�h\VXW�h�VXr�a\SOe�Y�cIYO_`V8Y-�\Zb^U�/YO_`^�e�_�YOa�r�moSU_�gq^Qfte�S � 2� ��s(��h=^�SU�=r�^;_`c�YOe�V8S-a�Y-��SIcU^Z8^QY-f=r"e�Sqe�h=^ moS-Z8ZbSI]�V8a\T�e�]�S�e�_�YOa�r�moSU_�gCYIe`VbSUa�_`[\Z8^QrQ�� FQGIP��KP ������� �m�e`h\^¹r��/r�e�^;g � WESUaUe�YOV8a=r�YOa¸^�ÐU[�YIe�V8S-a * 2� *le`h\^;a#_`^;�\ZXY-W;^ � �d���� -* 2��* �Us

� H�GIP �dD1F��� �m � W;S-a@e`Y-Vba=r�YOa5^QÐ@[=YIe`VbSUakSOm�e�h\^�moS-_`g �2�D*+�3]�h\^;_`^ *�VXr Y�cIYO_`VXYO�\Z8^

YOa�f �"V8r�a=SOeQ�\e�h\^Qa�_`^;�=Z8YUWE^ � �d�z® �� � 2� * ��²��+ * 2� � �@s��h\^;_`^�YO_`^{r��/r�e�^;gCr�]�h=V8W�hwYO_`^ [\a=r�S-Z8cIYO�\Z8^{YOa=fne�hd[=r�W;YOa=a\SOe��+^ e�_�YOa=r�moS-_`gq^QfnVba@e`S

r�S-Z8c-^QfnmoSU_�g�s���r�]"^{h=Y�cU^ e�StY�c-SUV8fna\SUaUe`^;_`gqVba=YOe�V8a\TC�\_`S/WE^Qf\[\_�^�r�]"^{h=Y�c-^ e`Stf/^Ee`^QW�er�S-gq^�e��d�\VXW;Y-Z3W;Y-r�^Qr"S-m[\a=r�S-Z8cIYO�\V8ZbVbe��-s� �mM]�^�_�^�WESUT-a\V8p;^�e�h\^ [\a=r�S-Z8cIYO�\V8Z8V}e��qSOm�Y�r��/r�e`^;g� ]�^ _`^Qf/[�WE^ V}e�e`S ®�]�h\^;_`^� ·W;Y-a���^{V8a@e�^;_`�\_`^Ee`^Qf�Y-r�Y��\À/^Qf�[\a=r�S-Z8cIYO�\Z8^{r��/r�e�^QgC²Es� �����������������»�/s¬�k®om�YOV8Zb[\_`^ _�[=Zb^�r`² ���^Ee � �+^�Y�r��/r�e`^;g S-m=e`^;_`g·^QÐ@[=YIe`VbSUa=r�YOa=f * 2� �

�+^�YOa�^QÐ@[=YOe�V8S-a�Vba � s� ��� *���H���N ����� ���� �m�*�YOa=f �YO_`^�mo[\a=W�e`VbSUa=YOZde`^;_`gCr�h�Y�c@V8a\T f/VbÇ+^Q_�^QaUe�Z8^QYUf/Vba=T�r��dg�j�+S-ZXr"e�h\^Qa � VXr�_�^Q�\ZXY-WE^�f��d�� �s

� HN-N-L�G.�CN+ �dN������ �m *{VXr�Y�cIYO_`V8Y-�\Zb^{rQs e�s * �� �"Y-a=f *{S/W;W;[\_�r�V8a ��e`h\^;aw_`^;�=Z8YUWE^ ��d�� �s �

�������������5�/s ~���K^;e� � � 2� F%J� 2� �3®$ \² ��2

� VXr�[\a�r�SUZbcIYO�=Zb^U��e`h\^;_`^�^EÀ/VXr�e�r�a\Snr�[\��r�e`V}e`[/e�V8S-a��nr;s eQs � � �� �tY-a=fI� � � �3®$ \² �\¿�moS-_SOe`h\^;_`]�VXr�^G � � �3®$ \² � � �3®$ �U²E��]�h=V8W�h¹VXr{V8g��+SUr`r�Vb�\Z8^-s���SI]"^;cU^;_��Ka\^;Vbe�h=^;_�®Rr��dg��+S-ZWEZXY-r�h�²�a\S-_¹®�SdWQWE[\_�r�W�h\^QW�i\²tV8r�Y-WEe�[=Y-ZbZ8�¸YO�=�\ZbVXW;Y-�\Z8^-s u"[/ewV}m�]�^ÅYO�=�\Zb� � 2� ¸Y-rr�[\�=r�e�Vbe�[/e`VbSUa �549 � e�S�e�h=^{SOe�h=^;_�^QÐ@[=YOe�V8S-a�]�^ SU�/e`Y-Vba�e�h=^{^QÐ@[\V8c�Y-Zb^Qa@e�r��/r�e`^;g

� Ï �+ � 2� F%# 2� �3®$ \² ��%]�h\VXW�hwW;YOa��+^{_�^�f/[=WE^�fte`S &cdVXY�®�S/W;WE[=_`r�W�h\^�W�i\²�s ���h\^t^EÀ\Y-g��=Zb^tY-��SIcU^qr�h\SI]�r�e`h=YIe�]"^Ca\^Q^Qf¹Y-f=f/V}e`VbSUa=YOZ�_�[\Z8^Qr{moS-_�f/^�WEVXf/V8a\Tw[\a\Vb��YIj

�\V8ZbVbe��wYOa=fnmoSU_�WESUgq�\[/e�V8a\TtgqS@r�e�TU^;a\^Q_`Y-Z3[\a\Vb�=^;_�rQs���h=^Qr�^�_�[=Zb^�r;�=f\^QWESUgq��S@r�Vbe�V8S-akY-a=f_`^;�\ZXY-W;^;gq^;a@eQ�\Y-_�^ V8a�m�Y-W�e�e`h\^{gqSUr�e�Vbgq�+S-_�e`YOa@e�S-a=^QrQs� J��dN-H�*���H��QP�FQPRH�D���� �^Ee�* 2� �"��^�Y-a�^�Ð@[=YIe`VbSUanV8a � rQs eQs�e`h\^;_`^ ^EÀ/V8r�e`r�Y�mo[=a=W�e`VbSUar��@g���SUZ�K �w%�� ��YOa=f�e�^Q_�gCr * 4 % 2�2 2 %3*'�1� � 4 % 2�2 2�% � ��]�V}e`h

*�� K�® * 4 % 2�2�2 % * � ²?%��� K�®��J4 % 2�2 2 % � � ²?2

��h\^Qan_`^;�\ZXY-W;^ � �d�Ce`h\^�r��dr�e�^Qg� Ï ��® �� * 2� � �I²�� -* 4 2� �J4 %�2 2�2 %3* � 2� � � ��2

� G.� ��� �\N�� *,�@D1F��� �K^Ee�* 2� ����^�Y-a�^QÐ@[=YIe`VbSUanV8a � rQs eQs®�|�² *{VXr�YqcIYO_`V8Y-�\Z8^�Y-a=f®R�-² *�f\S@^�r�a\SOe�S/WQWE[\_�V8a ��YOa�f®�¾U² *{S/WQWE[\_�r�Vba ��� -* 2� � �@s��h\^Qan_`^;�\ZXY-W;^ � �d�Ce`h\^�r��dr�e�^Qg

� Ï ��® �� * 2� � ��² * 4 � ���+-* 2� � ��2

Page 10: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

|Q  )1*O,/.1)+0123,/4k*-,/687+9;:=<� �����������������»�/s x����^Ee��°�+^ e�h=^ r�^Ee�S-m�_`[\Zb^�r�@®«e`_�V8cdV8Y-ZX²E�3®oS-_`V8^;a@e�²E�K®�r��@g���SUZKWEZXY-r�h�²��

®oS/WQWE[\_�r{W�h\^QW�i\²E��®�f\^QWESUgq��S@r�Vbe�V8S-a�²E��®�_�^Q�\Z8YUWE^Qg�^Qa@e�² �@sq �m � VXr�e�_�YOa=r�moS-_`gq^Qf5e�S � Ï�cdVXYYk_`[\Z8^tV8a�� ]"^t]�_�Vbe�^ ����� � ÏRsl%\S-_�e�h\^�_`^ �=^;ÀdV8c-^tY-a=fÅe`_`Y-a=r�Vbe�V8c-^nWEZ8SUr�[\_�^�SOm�e�h\^_`^;ZXYIe�V8S-a � � ]�^�]�_�Vbe�^ ���� s(�&r��/r�e`^;g � V8r�W;Y-ZbZ8^Qfl�«¤�¤���ÊI§=�;��ª;�b��Vbm�a\SUa\^�S-mKe�h=^�_`[\Z8^Qr"V8a�ÍV8r�Y-�\�\Z8V8WQYO�\Z8^�e�S � s V8r�V8_`_�^�f/[=WEV8�\Z8^ �@�nf/^E�=a=V}e`VbSUaKs ���W;W;S-_�f/V8a\T e�S e`h\^�f/^;�=a\Vbe�V8S-a=r�YO�+SIc-^-�-[\a\Vb��W;YOe�V8S-aCgq^QY-a=r�a\S-e�h\V8a\T{^;ZXr�^�e�h=Y-aq_�^�f/[=W�j

e�V8S-anSOmY�r��/r�e�^;g e�S�YOatV8_`_�^�f/[=WEV8�\Z8^�moSU_�g ®o]�h=^;_`^�YOanYO_`�\V}e`_`Y-_���S-_�f/^;_�SOm�Y-�\�\Z8V8WQYIe�V8S-a�rSOm�_`[\Zb^�r�Vba�¸V8r�YUf/gqV}e�e�^�f=²�s�������������5�/s Ì���'z^ e`YOiU^�e`h\^�r��dr�e�^Qg � mo_`S-g$�(À/Y-gq�\Zb^��\s ��]�h\^;_`^

� � ��1®0�+² 2� �1® �1®0(1²�²?% * 2� K�®$�&%J1d² ��2��h\^;a ����� � Ï(®�cdV8Y�®�f\^QWESUgq��S@r�Vbe�V8S-a�²�²"]�h\^;_`^

� Ï � � 2� �3®$(3²?% * 2� K�®$�&%J1d² � 2��SI]­®o_`^;�=Z8YUWE^;gq^QaUe�²�V8r�Y-�\�\Z8V8WQYO�\Z8^{YOa=f � Ï � � � Ï Ï��\]�h=^;_`^

� Ï Ï � � 2� �3®$(3²?% * 2� K�® �3®$(3²?%O1@² � 2� Ï Ï3VXr�V8_�_`^Qf/[�WEV8�\Zb^{Y-a=f�Vbawr�S-Z8c-^QftmoS-_`g�s ����;�C�I¤)(�����SOe�^qe`h=YIe�^Qc-^Q_��5r�S-Z8c-^�fkmoSU_�g V8r{V8_`_�^�f/[=WEV8�\Z8^-sn��aze�h=^CSOe�h=^;_{h=Y-a=fz^;c-^Q_��V8_�_`^Qf/[�WEV8�\Zb^�moSU_�g�V8r�^QV}e`h\^;_�Yqr�S-Z8c-^�fCmoS-_`g$SU_ �s� ������� ���­�/s �5®�[\a\Vb��W;YOe�V8S-a�e�h\^QS-_`^;gt²����É�X¦��C§/¡=� Æ"���I����¥I¡k¦�¢�¦����E� �(���«�$ �­�I� ��O¢�¦����;¤����«¡+�I���E¦ �$� È��o�\��¦�¢�¦����;� � �X¦�¦;¥O�¬©��UªE�8�t�o�\�;¡ ������ � Ï�¦ �8� � � Ï��X¦��«¡Å¦E¥O�¬©I�`Ê�ÈE¥I¤��Ä�O¡+Ê��o�\�¦�§=ª�¦����«�R§/����¥I¡5ÊU��Æ�¡+��Ê�ª;¢ � Ï"�X¦��C�C¥�¦��MË@�;¡+�;¤��I�¦E¥O�¬§/����¥I¡z¥�È � �

��������F��®Rr�iU^Ee`W�h+²%\SU_�Y�mo[\Z8ZK�\_`S@S-mMr�^;^Cv ��y�s(��h\^ g�S@r�e�V8adc-SUZbcU^Qft��YO_�e�VXr�e`^;_`g�V8a=YOe�V8S-aKs �m�]�^tida\SI] e�h�YIe�e`h\^�r��/r�e`^;gÄV8r�e�^Q_�gqV8a=YIe`Vba\TwSU[\_�e�Y-r�ilVXr�^�Y-r�Vb^Q_Q��YOZ8Z(_`[\Zb^�r�V8a��

�\_`^Qr�^;_`c-^�e�h\^�^QÐ@[\V8cIYOZ8^;a=W;^�S-m�r��/r�e�^QgqrQs(�dS�Zb^;e � Ï1�+^{YOanVb_`_�^�f/[=W;Vb�\Z8^�r��/r�e`^;g SU�/e`Y-Vba\^�fmo_`S-g � s� �m � Ï�� ·e�h\^Qa � Ï�YOa=f � Vbe`r�^;Zbm(YO_`^{[\a=r�S-Z8c�Y-�\Z8^-¿=^QZ8r�^ � Ï�g�[=r�e��+^�V8akr�SUZbcU^QfmoS-_`g³®«moSU_�SOe`h\^;_`]�VXr�^�Vbe ]�SU[\Z8f�a=SOe��+^�V8_`_�^�f/[=WEV8�\Z8^�²Es���hd[=r�e`h\^�r�[\�=r�e�Vbe�[\e�V8S-a5f/^;�=a\^�f�d� � Ï V8r�YqgqSUr�e�T-^Qa\^;_�YOZ3r�S-Z8[/e�V8S-a�SOm � Ï Y-a=f�S-m � Vbe`r�^;Zbm�s %'l^�h=Y�cU^�r�^Q^;a�VbaC��À\Y-g��=Zb^��/s ��h\SI]ºY-a�[\a�r�YOe�VXr���Y-�\Z8^�r�^Ee�S-m1W;Z8Y-[=r�^�r�W;YOa��+^�_�^;mo[/e�^�f

cdV8Yk[\a\Vb��W;YOe�V8S-a´Y-a=f¹WE[/e�s5��h\^t^;À\YOgq�\Z8^t��^QZbSI] r�h\SI]�r e`h=YIe�[\a\Vb��W;YOe�V8S-aµW;Y-a\a\S-e���^_`^Qr�e�_`V8WEe�^Qf�e�StYOe�SUgqr�S-mMf/VbÇ1^;_`^;a@e�WEZXYO[=r�^Qr��=[/e�g�[=r�e�YOZXr�S��+^�YO�\�=ZbV8^Qf�]�Vbe�h\V8awWEZXYO[=r�^QrQs�������������5�/s¬�����K^;e & � � 4 % � N � moS-_

� 4�� � "C®0�+²3%J"C®$ \²3%� N � "C®$(3²?%J"C®0*d² � 2

!�Z8^QYO_`Z8��&¹VXr�[=a=r�YOe�VXr��+YO�\Z8^-�1�\[/e ]"^�]�V8ZbZ�r�^Q^�e`h=YIe ]�V}e`h\S-[\e Y-a5Y-f\f\V}e`VbSUa=YOZ�e�^�W�h\a\VXÐU[=^� W;Y-a\a\SOe��+^�f/^;_`V8c-^QfKs�(c-^QawV}m�]�^��+^;_`g�[\e�^ "C®0�+²�YOa=f "C®$ \²�]�Vbe�h\V8a � 4 YOa=f "C®0(1²3%J"C®0*d²�]�V}e`h\V8a � N Y-a=f

e�_`��Y-ZbZ=[\a\Vb��W;YOe�V8S-a=r��+^Ee�]"^;^QatYIe`S-gCr�Vba � 4 Y-a=f � N ]�^�SU�/e`Y-VbaCY cIYO_`VXYOa@e�SOm1e�h\^�W;Z8Y-[=r�^� QK� "C®$�1² � "C®$ \²�s´u"[/e���gqS/f/[\Z8SÅc�Y-_�VXYO�=Zb^n_�^Qa=YOgqV8a\T=� � 4 ]�Vbe�h � Q�TUVbcU^Qr � 4 Y-a=f� N ]�V}e`h � Q�T-V8c-^�r � N s�'z^qr�^;^�e`h=YIe{WE[/e�e�V8a\T�S-[/e�r�Vba=T-Z8^�YOe�S-gCr f/Sd^Qr�a\S-e r�[/ÁtWE^�e`S

Page 11: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � |U|

f/^Q_�V8c-^�W;S-a@e�_�Y-f/VXW�e`VbSUaKs�'°h�YIe�]"^{a\^;^�f�V8r�[\a\Vb��W;YOe�V8S-aw]�Vbe�h\V8akYCWEZXYO[=r�^ moS-Z8Z8SI]�^�fn�d��YWESUa@e�_�Y-W�e`VbSUan_`[\Z8^-s�K^Ee�[�r�YO�\�=Zb�Ce`h\^�r�[\�=r�e�Vbe�[/e`VbSUa���� �549 ��e`S � 4 ¿de�h=^;a�]�^{SU�/e`Y-Vbane�h=^�WEZXYO[=r�^

� "C®$ \²?%O"C®$ \²?2u"[/e � "C®0 /²3%J"C®0 /²�_`^;�\_`^Qr�^;a@e�r�®��� \²E®�"C®$ \²+< "C®$ \²�²�]�h=V8W�hzV8r Z8S-TUV8WQYOZ8Zb�w^�Ð@[\VbcIY-Zb^QaUe e`S®E�F \²C"C®$ \²Es���hd[=r�]�^�gqY��{Y-�\�\Z8� W;S-a@e�_�Y-WEe�V8S-a{]�Vbe�h\V8a � "C®0 /²3%J"C®0 /²YOa=f�S-�/e�YOV8a � Ï4 � �"C®$ \²Es��dV8gqVbZXYO_`Z8��]"^�SU�/e`Y-Vba��d��� �� (549* ��e`h\^�WEZXYO[=r�^ � ÏN ��"C®0*d² � mo_�SUg � NUs���SI]¹�d�[\a\Vbmo�dVba=T "C®$ \²?%O"C®$*/²�cdV8Y�e`h\^�g�s T�s [s ���� 49* ��]�^�^Qc-^;a@e`[=YOZ8Zb��S-�/e�YOV8a � Ï Ï4 � � "C®0*d²YOa�f � Ï ÏN ��"C®$*/² � ]�h\VXW�h�_�^�r�SUZbcU^�e�S � cdVXY�YOe�SUg�VXW�WE[/e�s � Ï4 Y-a=f � ÏN YO_`^ W;YOZ8Z8^QfCm�YUW�e`S-_�rSOm � 4 Y-a=flSOm � N _�^�r��+^QWEe�V8c-^QZb�Us���h\^Cr�e`^;�=r Y-_�^�VbZ8Z8[=r�e`_`YOe�^�fkV8a5e`h\^Cf/^;_`VbcIYOe�V8S-a5�+^;Z8SI]® � r�e`Y-a=f\r"moS-_�r�[\�=r�e�Vbe�[\e�V8S-akY-r"�\_`^;��YO_�YIe�V8S-a�moS-_�e`h\^�WE[/e�Y-a=f�ηmoSU_�m�Y-W�e`S-_`Vba=T@²��

� "C®$�1²?%O"C®$ \²� "C®0 \² Î� "C®$*/² �

"C®0(1²3%J"C®0*d² �"C®$*/² � Î

� �;§/�

�� �����������������»�/s ¶l®om�Y-W�e`S-_�²����K^;e

� � � ��� 4 % 4 %�2�2 2 % � � % �F% � ��� 4® � � � 4 % 4 %�2 2�2 % � � % � % � ��� 4 � ��²��+^wYzW;Z8Y-[=r�^n]�h\^Q_�^ ��� |�Y-a=fµe`h\^ � ) YO_`^®o�+SUr`r�Vb�\Z8�w^;gq�/e��\²�r�^�ÐU[=^;a=W;^Qr�SOm�YIe`S-gCrQs��wSU_�^QSIc-^;_�Zb^;e �¹�+^�Y�gqSUr�e�T-^Qa\^;_�YOZ�[\a\Vb�=^;_SOm. 4 % 2�2�2 % ���@s���h\^;a

� Ï � � � ��� 4 �F%�2�2 2�% � � �F% � �® � ÏQ�� � �F% � 4 �F%�2�2 2�% � � � � � �K²"VXr�W;Y-ZbZ8^Qf�Y ÈE�-�;��¥O¤�SOm � s ����;�C�I¤)(��M �m�e`h\^�WEZXYO[=r�^�f/Sd^Qr�a=SOe(WESUaUe�YOV8a�cIY-_�VXYO�\Z8^QrMe`h\^;aCY�m�Y-WEe�SU_�V8r�SU�/e`Y-Vba\^�f���[=r�e(�d�WESUa@e�_�Y-W�e`VbSUanS-m�V8f/^Qa@e�VXW;YOZ�YIe�SUgCr;s� �m�V8a ��^E�=a\Vbe�V8S-a5�\s ¶ �+� |{e`h\^;a �zVXr�e�h\^�V8f/^Qa@e�VXW;YOZr�[\�=r�e�Vbe�[/e`VbSUatYOa=f�e�h\^�YOe�SUg 4�VXr��\[/e�e`S e�h\^�^;Àde�_`^;gq^�_�V8T-h@eQ�-_�^�r��+^QWEe�V8c-^;Z8�{Z8^Em«eQ�@SOm�e�h\^WEZXYO[�r�^UsM��hd[=r�]"^�YO_`^"[�r�V8a\T�m�Y-WEe�S-_`V8a\T{YOZXr�S�e�S{�+SUr�V}e`VbSUa�e`h\^�YIe`S-gCr�YIe�e`h\^�YO�\�=_�SU�\_�VXYIe`^�\ZXY-W;^Qr"moS-_�e`h\^ moS-Z8Z8SI]�Vba\TCW;[/eQs �� �����������������»�/s8|Q 5®��\V8a=YO_`�t_`^Qr�S-Z8c-^;a@e�²����^Ee � 4 � � 4 ��� 4 % YOa=f � N �B>%�� N ��� N

�+^{e�]�StW;Z8Y-[=r�^Qr�]�h\VXW�hkYO_`^ c�Y-_�VXYO�=Zb^�f/VXr���S-V8aUe�Y-a=f! ���B­��^�[\a\Vb��YO�\Z8^�]�Vbe�hwg�s T=s [Ks ��s��h\^Qane`h\^�WEZXYO[�r�^

�+4 �F%��N � ��� 4 �F% � N �VXr�W;Y-ZbZ8^Qf�YwªE�«¡1�I¤�¢t¤��E¦;¥I�¬©I�;¡=�KS-m � 4�YOa�f � NUs��m«e�^Q_�e`h\^Qr�^{�\_`^;�=Y-_`YOe�V8S-a=r�]�^�Y-_�^ _`^QYUf/�CmoS-_�e`h\^�f/^;�=a\Vbe�V8S-awSOm�e�h\^�T-^;a=^;_�YOZ1_�^�r�SUZb[\j

e�V8S-a�_`[\Z8^-s� �����������������»�/s8|-|n®�_�^�r�SUZb[\e�V8S-a�² ���^Ee � 4 % � N �+^�e�]"S�W;Z8Y-[=r�^�r�Y-a=f � Ï4 % � ÏN �+^�cIYO_`Vbj

YO�=Zb^{f/VXro��SUVba@e�cIYO_`V8Y-a@e`r�SOmm�YUW�e`S-_�r�S-m � 4 % � N�Y-a=f � �+^ Y��\V8a=Y-_��C_`^Qr�S-Z8c-^QaUe"SOm � Ï4 Y-a=f� ÏN s(��h=^;a � VXr�W;Y-ZbZ8^Qf�Yw®oTU^;a\^Q_`Y-ZX²�¤��E¦;¥I�¬©I�E¡��KSOm � 4�YOa=f � N-s

Page 12: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

|�� )1*O,/.1)+0123,/4k*-,/687+9;:=<u�� ��^;�=a\Vbe�V8S-a¸�/s8|-|�V}etVXrq�+SUr`r�V8�\Z8^�e`SÅf\^E�=a\^wV8a/�=a=V}e`^;Z8�´gCYOad�¹_`^Qr�S-Z8c-^;a@e�r�S-m�e�]"S

WEZXYO[�r�^�r;�+Y-r�e`h\^;_`^�Y-_�^{V8a/�=a\Vbe�^QZb��gCYOad�n��S@r�r�Vb�=Zb^�cIY-_�VXYO�\Z8^{_`^;a=Y-g�V8a\T@r;s�'z^�W;Y-akY�c-S-VXfe�h=V8r�^EÇ1^QWEe��d�¹Y5r�e`Y-a=f\Y-_`fÅ_`^;a=Y-gqVba\T5SOm�e`h\^�_`^Qr�S-Z8c-^QaUe��@�ÅcIYO_`VXYO�\Z8^Qr � 4 %�2 2�2 %#� ���Us�r�V8a\T�r�[=W�hzY�r�e`YOa�f\YO_�fw_`^;a=Y-g�V8a\Tne�h\^Q_�^�YO_`^�V8a=f/^Q^QflS-a\Z8�CÆ(¡=�«���;�¬¢n�C�I¡�¢�_`^Qr�S-Z8c-^QaUe�rSOmMe�]"SqW;Z8Y-[=r�^QrQs�������������5�/s x����K^;e

� 4�����®0��%J /² � "C®0�+²?%O"C®$ \²?%� N�� .C®$�1²?%J"C®HK�®$�1²�² � � ®0��%#�1²?2

��h\^QaK�d[\a=f/^Q_"Y�r�e`Y-a=f\Y-_`fq_`^;a=Y-gqVba\T��Oe`h\^�moSUZbZ8SI]�Vba=T�WEZXYO[=r�^Qr�YO_`^�_�^�r�SUZbcU^;a@e`r(SOm � 4�Y-a=f� N-�

� Q ���q®$� 4 %LK�®$��N�²�²3%O.C®0��N�² � "C®$�F4Q²?% � ®$��N %J��N�²?%��� ���q®�K�®0�F4Q²?%#��N�²3%O.C®0�F4Q² � "C®$��N�²?% � ®$� 4 %J�F4Q²?%��� ���q®�K�®0� 4 ²?%OK�®0� 4 ²�²3%O.C®0� 4 ² � � ®$� 4 %#� 4 ²32 ���h\^"moS-Z8ZbSI]�V8a\T�f\^Qf/[=WEe�V8S-a��\_`Vba=W;Vb�=Zb^"S-a�WEZXYO[=r�^�Z8S-TUV8W�V8r�W�h=Y-_`YUW�e`^;_`VbpQ^Qf �d�{[=r�Vba\T�S-a=Zb�

S-a=^�r�V8a\T-Z8^ Vba\mo^;_`^;a=W;^�_`[\Z8^-�\a�YOgq^;Z8�t_`^Qr�S-Z8[/e�V8S-aKs� �����������������»�/s8|��k®�_�^�r�SUZb[\e�V8S-a�f/^Qf/[�W�e�V8S-a+²����Å_�^�r�SUZb[\e�V8S-a{f/^Qf\[=W�e`VbSUaq®R��j�f/^Qf/[�W�e�V8S-a+²

SOmY�WEZXYO[=r�^ � mo_�SUgÉY�r�^;e�SOmKWEZXYO[�r�^�r�&�VXr�Y�r�^�ÐU[=^;a=W;^�SOmKWEZXYO[�r�^�r � 4 % 2�2�2�% � ��]�V}e`hCe�h\^moS-Z8Z8SI]�Vba\Tq�\_`S-�+^;_�e�V8^QrQ�|-s � � � � s�/s�%\SU_�^;cU^;_`�$+�]�Vbe�h + � U| %�2�2 2 %��/��]"^{h=Y�c-^U��^;Vbe�h\^Q_ � ) VXr�YCWEZXYO[�r�^{V8a &lSU_ � ) V8rY�_�^�r�SUZbcU^;a@e�SOme�]"SCWEZXYO[=r�^Qr ��� % � - ]�Vbe�h %3,�� +`s

��aw��j�f/^�f/[=W�e`VbSUa�SOm � mo_`S-g'&zV8r�WQYOZ8Zb^�fnY-aw��j�_`^Emo[\e`YIe`VbSUanS-m &�s ��������������5�/s ¶����K^;e

&5� � "C®$�&%OK�®0�+²�²E¿�"C®0M�%J*d² � .C®0*d²E¿�.C®01d² � � 2��h\^Qa

�� � "C®$�&%OK�®$�1²�²E¿�"C®0M�%#*/² � .C®$*/²�¿ � .C®HK�®0M/²�²E¿�.C®01d² � ¿ �VXr�YOa���j�_�^;mo[/e`YOe�V8S-a�SOm�&�s� �a�e�_`^;^�moSU_�gCYIe kV8r�S-m�e`h\^ moS-_`g

� "C®0��%OK�®0�+²�² "C®0M�%#*/² � .C®0*d²� .C®�K�®�Md²�² � .C®�1@² �

� �

�wS/f/[\Z8SÅe�h\^5W;Z8Y-[=r�^nmoSU_�g e�_�YOa=r�moS-_`gCYIe`VbSUa� W;Y-aº�+^5WESUa=r�V8f/^Q_�^�fºYUrtYz�\_`S@S-m��d�WESUa@e�_�Y-f/VXW�e`VbSUanS-me�h=^ moS-_`g�[\ZXY

vb®����1²E®��! /²#"C®$�&%# \²�'z®��)(3²E®���*/²E®�"C®$(+%#*/²-,/.C®0*d²�²�y , ®��!1d²#.C®�1@²32����^Qr�S-Z8[/e�V8S-a�V8r"Y�W;S-gq�\Z8^Ee�^�Vba\mo^;_`^;a=W;^��\_`Vba�WEV8�\Zb^�S-a�W;Z8Y-[=r�^�ZbSUT-VXW�YOa�f3�@e�S-TU^Ee`h\^;_�]�V}e`h

a\SU_�gCYOZ-moS-_`g#e�_�YOa=r�moS-_`gCYIe�V8S-a�r;��Y�_�^;mo[/e`YOe�V8S-a=Y-ZbZ8� WES-gq�\Z8^Ee`^�V8a/mo^;_`^;a�WE^�r��/r�e`^;g moS-_�=_`r�e�jS-_�f/^Q_�ZbSUT-VXWOs� ������� ���­�/s ¾�� ����¦;¥O�¬§/�R��¥O¡·�X¦�W;S-gq�\Z8^Ee`^ �n���«��� � È�&��X¦Å�O¡ §/¡\¦;�O�R�X¦oÆ��UªE�8�z¦;�E�n¥�È

�;�b�I§d¦;�E¦��«�=�E¡k�o�\�;¤����� U�X¦��R¦{�O¡ ����¤��RÈ�§/���I����¥I¡l¥�È & �

Page 13: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � |�¾

��������F��'z^tgq^;_`^;Z8�kT-V8c-^�e`h\^CgCYOV8azZ8V8a\^CSOm"e�h\^��\_�SdS-m�¿MY�f/^;e`YOV8Z8^Qfz�\_`S@S-m�WQYOaz��^moS-[=a=f�Vba¹v ¾- Iy�su�����^;_`�\_�YOa=fK r�e�h=^;S-_`^;g Y�r�^Ee�S-m+WEZXYO[�r�^�r &nV8r�[\a�r�YOe�VXr���Y-�\Z8^"VbÇte`h\^;_`^�^EÀ/V8r�e`r�Y��=a\Vbe�^

r�^Ee &KÏKS-m�T-_`S-[\a=fÅ®�VRs ^-s�cIYO_`V8Y-�\Z8^Ej�mo_�^Q^�²"WEZXYO[=r�^QrQ�\SU�/e`Y-Vba\^�f��d��V8a=r�e�YOa@e�VXYIe`VbSUawSOm(WEZXYO[�r�^�rV8a &���]�h=V8W�hwVXr�[=a=r�YOe�VXr��+YO�\Z8^-s���hd[=r�e�h=^�[\a=r`YIe`V8r���Y-�\VbZ8Vbe��nS-m�e�h\^��=_`r�e�j�S-_�f/^Q_��\_`S-�\Z8^;g&lVXr�_`^Qf/[=W;^Qf�e�Sqe`h=YIe�S-me�h=^{�\_�SU��S@r�Vbe�V8S-a�YOZ1�\_`S-�\Z8^;g%& Ï s��h\^;akVbe�VXr��=_�SIcU^Qfne�h=YOe�_`^Qr�S-Z8[/e�V8S-a�VXr�W;S-gq�\Z8^Ee�^�S-akr�^Ee`r�SOm�T-_`S-[=a=fwWEZXYO[=r�^QrQs���r�Y

WESUa=r�^QÐ@[\^;a�WE^�e�h\^Q_�^ ^;ÀdVXr�e`r�Y-a���j�_`^Emo[/e�YIe�V8S-a +ÏKS-m &KÏ�s%�V8a=Y-ZbZ8�te`h\^{_�^;mo[/e`YOe�V8S-a +Ï3VXr{�¬� È����`Ê e�SCY�_�^;mo[/e`YOe�V8S-a wS-m &�s(�KVbm«e�V8a\TCVXr�Y�e�^�W�h\a\VXÐU[=^

_`^;�\ZXY-W;Vba\T�Y{_`^Qr�S-Z8c-^;a@e � Ï+S-mKVba=r�e`Y-a=WE^�r � Ï4 % � ÏN S-m�WEZXYO[�r�^�r � 4 % � N��d�CY{_`^Qr�S-Z8c-^;a@e � SOm� 4 % � N{r;s eQs � Ï3VXr�Y-anV8a=r�e`YOa�WE^{SOm � s

%��h\^�ZbVbm«e�V8a\Tz�\_�V8a=W;Vb�\Z8^�V8r�e`h\^ngqS@r�eCr�V8T-a=V}��WQYOa@e�mo^QYIe`[\_`^�SOm��=_�r�e�j�SU_`f/^Q_�_`^Qr�S-Z8[/e�V8S-as

�a=r�e�^�Y-fkS-m(�\_`Sdf\[=WEV8a\T�Vba/��a\V}e`^;Z8�wgCYOad��_�^�r�SUZbcU^;a@e`r�SOm(V8a=r�e�YOa=W;^Qr�SOm(e�]"SnW;Z8Y-[=r�^Qr�V}e V8r^;a=S-[\TUh�e`S�[=r�^�e�h\^�T-^;a=^;_�YOZ\_`^Qr�S-Z8c-^QaUe�rM]�h\V8W�htY-_�^���Y-r�^Qf�S-aqgqSUr�e�T-^Qa\^;_�YOZ/[=a\V}�+W;YIe`VbSUaS-a=Zb�Us�'l^{TUVbcU^ Yqr�Vbgq�\Z8^{^EÀ\Y-g��=Zb^ V8ZbZ8[=r�e�_�YIe�V8a\T�e�h=V8r��=_�V8a=WEV8�\Z8^-s�������������5�/s8|Q ����^Ee

&5� � "C®$�1²�¿ "C®$(3² � .C®$(3²�¿ .C®HK�®01d²�² � ��2�K^;e ���+^�YOa�YO_`�\Vbe�_�YO_`�CT-_`S-[\a�fCe�^Q_�g�SIc-^Q_�e`h\^�r�VbTUa=YIe`[\_�^ K�%OM �{Y-a=f

& Ï � � "C®HK�®���²�²�¿ "C®�K�®���²�² � .C®HK�®���²�²E¿�.C®�K�®���²�² � ��2��h\^;a

� � � "C®�K�®���²�²E¿ "C®�K�®���²�² � .C®�K�®���²�²�¿ � .C®HK�®���²�²�¿�.C®HK�®���²�² � ¿ �VXr�YOa���j�_�^;mo[/e`YOe�V8S-a�SOm�&3ÏRs(u"[/e

��� �54/K�®���²3%#( 4 K�®���²?%O1 4 � �moS-_

� � "C®$�+²E¿ "C®$(3² � .C®$(3²�¿ � .C®$(3²�¿ .C®HK�®���²�² � ¿ � 2u"[/e wVXr�Y-a���j�_`^Emo[/e�YIe�V8S-a�SOm�&�s �

>��A�������H��RLF�P�H+D �\DMJ ��ÅA�KAR?�A����ÅN ���RN-L���L�� ��ÅA ��_�Y-f/Vbe�V8S-a=Y-Z�Z8S-TUV8W�W;YOZXWE[=ZbV�]"S-_`inSUawe�h\^�mo[\Z8Z�r��da@e`YOÀwSOm

Z8S-T-VXW�YOa�f�a=SOe(S-aqa\SU_�gCY-ZdmoS-_`gqrQs���h\V8r(h=Y-r�e`h\^�Y-f\c�Y-a@e`YOTU^"e�h=YOe(e�h\^�Z8S-TUV8WQYOZ\r�e�_`[=W�e`[\_`^SOm3e`h\^�e`h\^;SU_�^Qgqr�V8r��\_`^Qr�^;_`c-^QfqY-a=f�e�h\^�r�^QgCYOa@e�VXW;Y-Z\gq^QYOa=Vba\T�V8r�]�^QZbZbj��\_�^�r�^Qa@e�^Qf�V8aqe�h\^f/VbÇ+^Q_�^Qa@eqr�e�^Q�=r�SOm�Ylf/^;_`VbcIYOe�V8S-aKs¹��h\^�_�^�r�SUZb[\e�V8S-a´WQYOZXWE[\Z8[=rQ��Vba»WES-a@e`_`YUr�e���]�SU_�i/r�SUar�Vbgq�\Z8^ta\SU_�gCYOZ(moS-_`gqr�]�h\V8W�hzm�Y�cUS-_{^EÁtW;Vb^QaUe�Vba/mo^Q_�^Qa=WE^U���=[/e�S-aze`h\^tSOe`h\^;_�h=YOa=fzVbe`rf/^Q_�V8cIYIe�V8S-a�r�Z8SdS-iC[\TUZb�tY-a=fµ¯�[\a\a=YOe�[\_�YOZX±\s��wSU_�^QSIc-^;_�]�^�^;cU^;an_�VXr�iqe`SqZbS@r�^ r�e`_�[�W�e�[=_`Y-ZV8a/moS-_`gCYIe�V8S-a�]�h\VXW�h�VXr�[�r�^;mo[\ZdVbaqf/^E��a\Vba=T�TUS@S/f�YOa=f��IS-_Mr�h\SU_�eM�\_`S@S-m�r;s�'l^�]�V8ZbZ/r�h\SI]¹V8ae�h=V8r(r�^QWEe�V8S-a�e�h=YOe�e�h\^Q_�^�VXr�Y�_�^Qgq^Qf/�{moSU_�e�h\VXr(f/^;mo^QWEe(SOm1_�^�r�SUZb[/e`VbSUaK�Ia=Y-g�^QZb��r�e`_�[�W�e�[=_`Y-ZWEZXYO[�r�^�moS-_`gÉe�_�YOa=r�moS-_`gCYIe�V8S-asM��h\VXr�e�^�W�h\a\VXÐU[=^�Y-ZbZ8SI]�r([=r�e`S�f/^;�=a\^ YOaº¯�V8aUe`^;_�m�Y-W;^Q± e`Sr�e`YOa�f\YO_�f�ZbSUT-VXW�W;Y-Z8W;[\Z8V�YOa�f�e�Sw¦���¥I¤���e�h=^�r�e�_`[=W�e`[\_�^�SOm�mo[\Z8Z��_`r�e�j�S-_�f/^;_�Z8S-TUV8W�]�V}e`h\S-[/er`Y-WE_`Vb��WEV8a\T5^;ÁtWEV8^;a=W;�-s´��rl¯�e�_�Y-f/Vbe�V8S-a�YOZX±wZbSUT-VXWnWQYOZXWE[\Z8[=r�]�^�W�h\SdSUr�^���^Qa@e�p;^QaK r ���+^QW;Y-[=r�^tV}e�V8r�e�h=^�gqSUr�e�^;Z8^;T@YOa@e�YOa�f·¯�r�^;gCYOa@e`V8WQ±wW;YOZXWE[=Zb[=r�moS-_�WEZXY-r`r�VXW;Y-Z��=_�r�e�j�SU_`f/^Q_Z8S-T-VXWOs���h\^{^QZb^Qgq^;a@e`r �� VXr�]"S-_`i@V8a\T�]�V}e`hwYO_`^ r�^QÐ@[\^Qa@e`rQ�

Page 14: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

|2� )1*O,/.1)+0123,/4k*-,/687+9;:=<� �����������������º¾\s8|�®Rr�^�ÐU[=^;a@e�² ���Är�^�Ð@[\^;a@e�V8r�YOa ^EÀ/�\_`^Qr`r�V8S-a°S-m�e`h\^5moSU_�g � ���

]�h\^Q_�^ �ÃYOa=f � Y-_�^��=a\Vbe�^Cg�[\Zbe�VXr�^;e`r{S-m"���KjRmoSU_�g�[\ZXY-r�®oV�s ^Us�e�]"Swr�^�Ð@[\^;a@e`r � 4 ��� 4YOa�f � N � � N Y-_�^�WES-a�r�VXf/^;_`^Qf�^�ÐU[�YOZVbm�e�h=^�g�[=Z}e`V8r�^Ee�r�_`^;�\_`^Qr�^;a@e`^Qf��d��� 4 YOa�f��@��� NYO_`^ ^QÐ@[=Y-ZKYOa=fne�h=SUr�^�_`^;�=_�^�r�^QaUe`^Qf��@� � 4 % � N{Y-_�^{YOZXr�S�^�ÐU[�YOZ«²�s ���SOe`^ e�h=YOe�WEZXYO[=r�^Qr�Y-_�^ r�^QÐ@[\^;a@e�r�WES-a@e�YOV8a\Vba=T�SUa\Z8��YIe`S-gqV8W�moSU_�g�[\Z8YUr;s

� �����������������º¾\s �5®oe�h\^�WQYOZXWE[\Z8[=r �� ² ����h\^qVba\Vbe�VXYOZ�r�^�ÐU[=^;a@e`r{Y-_�^� � ÉmoSU_ �=_`r�e�jS-_�f/^Q_�moS-_`g�[=Z8YUr� �sl �a¹e�h=^n_`[\Z8^Qr�S-m �� ]"^nY-Zb]�Y��/r{gCYO_`i5e`h\^nY-[/À/VbZ8V8Y-_��lmoS-_`g�[=Z8YUr®oV�s ^-s�e�h=^�moS-_`g�[=Z8YUr�Vbate�h\^��\_�^QgqV8r�^U®Rr`²�[�r�^�f�moS-_(e`h\^�V8a/mo^Q_�^Qa=WE^�²(YOa�f�e�h\^��\_�V8a=W;Vb�=Y-Z�®�VRs ^-se�h=^�V8a/mo^Q_�_`^Qf=²�moS-_`g�[\ZXYt[�r�V8a\T�f/V}Ç1^;_`^;a@e gCYO_`i@V8a\T�r��dg��+S-ZXrQs���hd[=rQ�3VbalS-[\_ f/^;�=a\Vbe�V8S-aK�'�j�Vba@e�_`S/f/[=WEe�V8S-a�e�S�e�h=^{_�V8T-h@e�e`Y-i-^Qr"e`h\^ moS-_`g

�+4 � � % � ��N ��� N %OB ��+4 %��N ��� 4 % A' B � % � N 'º���

'l^�[=r�[=YOZ8Zb��Y�c-SUV8f�gCY-_�idV8a\TUr��@���\[/e�e�V8a\Tne�h\^�YO[/À/V8ZbVXYO_`��moSU_�g�[\ZXY-r�YOe�e`h\^�Z8^Em«e`g�S@r�e�+SUr�V}e`VbSUa�V8a�e�h\^�YOa@e�^�WE^Qf\^;a@e�SOm�r�^�ÐU[=^;a@e`r�Y-a=f�Vba�e�h=^{_�V8T-h@e�gqS@r�e��+SUr�V}e`VbSUa�V8a�e�h\^�W;S-a/jr�^QÐ@[\^;a@e�SOmr�^QÐ@[\^QaUe�r;s���h\^��\_`Vba=W;Vb��YOZ�moS-_`g�[\ZXY�gqSUr�e�Z8�qV8r�VXf/^;a@e�Vb��Y-�\Zb^��d��e�h\^ WESUaUe`^EÀdeQs��hd[=r�e`h\^{_�[=Zb^{YO�+SIc-^�]�V8ZbZK�+^{]�_`V}e�e�^;awYUr

�+4 ��� 4 % ��N ��� N %JB�;4 %��N ��� 4 % � N % ' B '´���

��h\^�cU^;_�r�V8S-a�SOm �� ]"^�Y-_�^{[=r�V8a\Tth\^Q_�^{VXr�e`h=YIe�Vbaµv �Oy�YOa=fwr�ZbV8T-h@e`Zb��f/^;cdVXYIe�^�r�mo_`S-g��^;a@e`p;^;a r"S-_`V8T-V8a=YOZ+c-^Q_`r�VbSUakv}|I��y�s���h\^�f\V}Ç1^;_`^;a=W;^Qr"h\SI]"^;cU^;_�Y-_�^�]�V}e`h\S-[\e"V8gq��SU_�e�YOa=W;^e�S�e�h=^�_`^Qr�[\Zbe`r"�\_`^Qr�^;a@e�^�fCVba�e�h\VXr�r�^�W�e`VbSUaKs���^QYUf/^;_�r(]�h\SqYO_`^�V8a@e�^Q_�^�r�e`^QfCV8anY�f/^Ee�YOV8Zb^�ff/^;�=a\Vbe�V8S-a�SOm �� YO_`^�_`^Emo^Q_�_`^Qf�e�Swvb|���yKS-_�e�Swv ¾-xOy ���h\^ gqY-Vban_�^�r�[=Z}e"SOmM��^QaUe`p;^QaK r�m�Y-g�SU[=r"�=YO�+^;_ vb|���y3]�Y-r�e�h\^ WE[\e�j�^;Z8VbgqV8a=YIe`VbSUate�h=^;SOj

_`^;g�s� �e�r�h=SI]�r�e`h=YIe��\V8a�Y-_��=V}e`_`Y-_�� �� j��\_`SdSOm�rQ�@e�h\^�W;[/e�_�[=Zb^

�;4 ��� 4 % %���N ��� N�+4 %��N ��� 4 % � N �E§/�

W;YOa¹�+^t^QZbV8gqVba=YOe�^�f3¿�e�h=^t_�^�r�[=Z}e�VXr�Yw�=_�SdSOm�]�Vbe�h¹e`h\^w¦�§=ª�ÈE¥O¤���§/�8�q¨1¤�¥`¨=�E¤���¢I��V�s�^Usb�e�h=^C]�h\S-Z8^C�\_`S@S-m�VXr gCY-f/^CS-m�e`h\^tr��da@e`YUW�e`V8W�gCYIe`^;_`V8Y-Z�SOm�e`h\^C^;a�fzr�^QÐ@[\^Qa@eQstu"�we�h=V8r�\_`S-�+^;_�e��»��^QaUe`p;^QaK rnWE[/e�jRmo_`^;^ �� W;Y-a»�+^k[=r�^Qf°YUrtY¹�=YUr�VXrqmoSU_t�\_`S@S-m�r�^�YO_�W�h»Y-a=fYO[\e�S-gCYOe�^Qfzf/^�f/[=W�e`VbSUaÅ]�h\^;aÅWESUg��\V8a\^Qfl]�Vbe�hze�h\^C[=a\V}�+W;YIe`VbSUal�=_�V8a=WEV8�\Z8^-¿�e�h\^tW;S-_`_�^;jr���SUa=f/V8a\T�W;Y-Z8W;[\Z8[=r�VXr�e�h\^����UªE�b���O§ �����O�b�E§/�}§d¦�v �-��y�s�%\S-_�V8Z8Zb[=r�e�_�YIe`VbSUa�]�^�TUVbcU^{Ytr�V8gq�\Z8^WE[\e�j�mo_�^Q^ �� j��\_�SdS-m�SOm�e�h\^�r�^QÐ@[\^Qa@e

"C®0M/²?%�®E�F�+²E®�"C®$�1² , "C®HK�®$�+²�²�² � "C®HK N ®0M/²�²

]�h\VXW�h¹®�r�^;gCYOa@e�VXW;Y-ZbZ8�\²"r�e�YOa=f\r"moSU_�e�h\^ moSU_�g�[\ZXY

v "C®0M/²�'l®E�F�+²E®�"C®$�1² , "C®HK�®$�+²�²�²�y , "C®HK N ®0M/²�²?2

Page 15: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � |�~

"C®0M/² � "C®0M/²"C®�K�®�M/²�² � "C®�K�®�Md²�² "C®�K N ®0M/²�² � "C®HK N ®0M/²�²"C®HK�®0M/²�²3%J"C®�K�®�M/²�²-, "C®HK N ®�Md²�² � "C®�K N ®0M/²�² ,¸���

"C®HK�®0M/²�² , "C®�K N ®0M/²�²3%J"C®0M/²-,/"C®�K�®0M/²�²�²?%O"C®0M/² � "C®�K N ®0M/²�² ,¸���®E���1²E®�"C®$�+² ,/"C®�K�®0�+²�²�²?%O"C®0M/²-, "C®HK�®0M/²�²�²?%O"C®0M/² � "C®�K N ®0M/²�² �k���

®E�F�+²E®�"C®$�1² , "C®HK�®$�+²�²�²3%Q®E�F�+²;®0"C®$�1² , "C®HK�®$�1²�²�²3%J"C®�Md² � "C®�K N ®�M/²�² �k���®E���1²E®�"C®$�+² , "C®�K�®0�+²�²�²?%O"C®0M/² � "C®�K N ®0M/²�² � ���

�KA �3A��KF;GIL�N-FQL�G.������� �=L � �,-�H=G.*°A ��h\^Ci-^Q�ke�Ske�h\^w¦��«��§/�b�I����¥I¡5SOm�WE[/e�jRmo_`^;^ ���d�5_`^Qr�S-Z8[/e�V8S-alV8r{e�h\^�¦���¤�§=�E��§/¤��I��¡1¥I¤��C�I�=ÈE¥O¤�� e�_�YOa=r�moS-_`gCYIe`VbSUaKsq �aÅW;S-a@e�_�Y-r�e�e�S�e�h\^r�e`YOa�f\YO_�fCa\SU_�gCYOZ�moS-_`gÉe�_�YOa=r�moS-_`gCYIe`VbSUaC�\_�^�r�^Qa@e�^QftVban�/[\�=r�^QW�e`VbSUa��\sb|�e�h\^ r�e`_�[�W�e�[=_`Y-ZS-a=^�VXr��=Y-r�^QfwSUa5V8a@e�_`Sdf\[=W�e`VbSUa=r�S-m�a\^Q] �\_`^Qf/VXW;YOe�^qr��dg��+S-ZXrQs �^Ee{Î �+^�e`h\^�moS-_`g�[\ZXYe�S´��^5e�_�YOa=r�moS-_`gq^Qf»Vba@e`SµWEZXYO[=r�^wmoS-_`g�s·��h\^kVXf/^QYÅVXrCe`h\^kmoSUZbZ8SI]�Vba=T¹S-a\^U�l%\SU_�YOad�r�[\�/moS-_`g�[=Z8Y( &V8a�Î WE_`^QYOe�^{Y�a\^;]#�\_`^Qf/VXW;YOe�^{r��dg���SUZ�"��ºYOa=f»¯�f\^E�=a\^�± "�µ�d� ���d[\�=��S@r�^U�\moS-_�VbZ8Zb[�r�e`_`YOe�V8S-aK�/e`h=YIe �� 4� �N moSU_� � ' %L< %L, ��YOa=fne�h�YIe� VXr�e�h\^r�^Ee{SOm�cIY-_�VXYO�\Z8^Qr�mo_`^;^�Vba �s�%=[\_�e�h\^Q_�gqS-_`^�Z8^Ee�����^�e�h=^qr�^Ee SOm�c�Y-_�VXYO�=Zb^�r�mo_`^;^qV8a 4YOa�f��&e`h\^�r�^Ee�SOm(cIYO_`VXYO�\Z8^Qr�mo_`^;^�Vba �NOs���h\^;alWEZ8^QYO_`Z8�� ��� ����s ��^E�=a=^�c-^�W�e`S-_�rSOm�cIYO_`V8Y-�\Z8^Qr���&%�� �%��1�mo_�SUg e�h=^�r�^;e`r� %��-%��{s���h\^Qa�e`h\^�Ê-�RÆ(¡��«¡@Ë�ÈE¥I¤���§/�b��moSU_ "��´V8rQ�

®E����1²Ev "���®���1²�� ®0"���I®�� \²� "�! -®��1U²�²�y 2�dV8gqVbZXYO_`Zb�le�h=^nf/^;�=a\V8a\TwmoS-_`g�[=Z8Y�moSU_� � ";B VXr�®�����1²E®0" � ®���1²"� ";"�#�®���1²�²�Y-a=fzmoS-_ � ®�. \²CB­Vbe�VXr

®E�$��+²E®�" � ®���1²�� ®�. \²C"#�®����%J \²�²?2��S-e�^le�h=YOe�e`h\^zf\^E�=a\V8a\T´moS-_`g�[\ZXY-r���[=r�e�_`^;�\_`^Qr�^;a@enY´gCYIe�h=^;gCYIe`V8WQYOZ�e`SdS-Z ]�h\VXW�h¸V8r]�VXf/^;Z8��[=r�^QfnV8a�gCYOe�h\^QgqYOe�VXW;rQ�\a=Y-g�^QZb�z�� U���E¡=¦���¥O¡lª;¢�Ê-�RÆ(¡=�«����¥I¡�s���h\^ ^EÀde`^;a=r�VbSUa�moS-_�jg�[=Z8YUr�f/Vb_`^QWEe�Z8���dV8^;ZXfte`h\^�r�e`_�[�W�e�[=_`Y-ZKWEZXYO[=r�^�moS-_`g�s� �����������������º¾\s ¾����^Ee�Î �+^qY�W;ZbS@r�^�f�moS-_`g�[=Z8Y�YOa=f&% ��^�e`h\^�r�^Ee{S-m�YOZ8Z(f/^E��a\Vba=T

moS-_`g�[=Z8YUr�SU�/e`Y-Vba\^�fÃmo_`S-g Îqs ��h\^;aÍe�h\^´¦���¤�§=�;�R§/¤��O���;�b�I§d¦;�qÈE¥O¤��ÄS-m�Î VXr�e`h\^År�^;e')(+*-,/.10 ®RÎ�²�f/^E��a\^Qf��d�

' (+*-,-.�0 ®�Î�² �32 '54 ®0B�²16 B�7%5���+ � �8.�]�h\^Q_�^ '54 VXr�e`h\^�S-�+^;_�YIe�SU_�S-m(e�h\^qr�e`YOa�f\YO_�fkWEZXYO[�r�^�moS-_`g e�_�YOa=r�moS-_`gCYIe�V8S-akY-a=fkV8alY-ZbZf/^;�=a\V8a\TqmoS-_`g�[\ZXY-r ')4 ®:9;�=<5²"V8r�f/^E�=a=^Qf��d� '54 ®�®:9D,=<5²�'l®-< ,=9�²�²�s�KV8i-^ ')4 YOZXr�S ' (+*-,-.�0 VXr(r`YIe`V8r���YO�=VbZ8V}e����\_`^Qr�^;_`c@V8a\T{YOa�f�e`hd[=r(]"^QY-i@Z8��W;S-_`_�^�W�e�®�Y�moSU_�gCYOZ

�\_`SdSOm�W;Y-a¹��^nmoS-[=a=f¹V8aÍv}|���yo²�sz%\S-_��\_�Y-W�e`V8WQYOZ�_�^�Y-r�S-a=r�S-a\^�WQYOa´Y�cUS-VXfle�SlW;S-a=r�e�_`[=WEef/^;�=a\V8a\T�moS-_`g�[\ZXY-rmoS-_�YIe`S-gCrQs���h\^�r�^�]"S-[\ZXf�h=Y�cU^(e`h\^"moS-_`g ®E����1²E®�" # ®���3²��/.C®���3²�²Es� �eVXr�^QY-r���e�S r�^Q^�e`h=YIeMe�h=V8r�_`^Qr�[\Zbe`rMS-a\Z8�{V8a�Y�_�^Qa=YOgqV8a\T�S-m\e�h\^�YOe�S-gCr�e�h=^;gCr�^QZbcU^Qr�gCYOidVba=Te�h=^�W;S-_`_�^�r��+S-a=f\Vba\TtW;Z8Y-[=r�^Qr�_`^Qf\[\a=f\Y-aUe�s���h\^�r�e`_�[=WEe�[\_�YOZ�a\S-_`gCYOZmoS-_`g r�[\�/��^�W�e`^Qf�e`Se�h=V8r�V8gq�\_`SIc-^;gq^QaUe�VXr�f/^;a=SOe�^�f��@� ' Ï(+*:,/.�0 ®�Î�²Es�������������k¾\s8|����K^;e�Î � ®E�F�+²C"C®0�+²�<z®�"C®0M/²�'I.C®:>;²�²�s

��h\^�f/^;�=a\V8a\TqmoS-_`g�[=Z8YUr�®�S-gqVbe�e�V8a\Tqe`h\^�YIe`S-gqV8W�Z8^;cU^;Z«²�YO_`^�e`h\^ moS-Z8ZbSI]�V8a\TqS-a=^QrQ�� 4 � 8 � ® 4 < N ²?%� N � 4 � ®����1²C"C®$�1²?%� Q � N � ®�"C®0M/²�'I.C®?>E²�²32

Page 16: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

|QÌ )1*O,/.1)+0123,/4k*-,/687+9;:=<'z^{a\SI] W;S-gq�\[/e`^ e�h\^�r�e`Y-a=f\YO_�f�WEZXYO[=r�^�moS-_`gqr#& ) � ' 4 ® � ) ²�YOa=f�SU�/e`Y-Vba

&�4�� �8 � 4 % �N-¿ 4 � �8�¿ �N � �8.��%&�N�� 4 � "C®0�+²E¿ "C® � ² � 4 � %& Q � �N � "C®�M/²�¿ �N � .C®?>E²�¿ "C®�Md²3%O.C®?>E² � �N � 2

��SI]' Ï(+*-,/.10 ®RÎ�² � � �8.� ��&�4 � &�N�� & Q 2

��SOe`^Ce�h�YIe�V8aµWESUg��=[/e�V8a\T!&�NC]"^Ch=Y�c-^qe`S5YO�=�\Zb�zr�iUS-Z8^;gqV8pQYIe`VbSUazY-a=fze�hd[=r�S-�/e�YOV8ae�h=^{a\^;]&WESUa=r�e�YOa@e�r��dg���SUZ � s � �a ��À\YOgq�\Z8^µ¾\s8|Åe�h=^ºr�e�_`[=W�e`[\_`Y-Z�WEZXYO[�r�^¹moSU_�g WESUa=r�VXr�e`rkS-mCa\Vba=^´WEZXYO[=r�^QrQ�{]�h\V8Zb^

' 4 ®RÎ�² � � "C®$�1²?%O"C®0M/²�¿ � "C®$�1²?%O.t®:>E² �wY-a=f¹e`hd[=rCWESUa=r�VXr�e`r�SOm�e�]"SlW;Z8Y-[=r�^Qr�S-a\Z8�-s �e�gqV8T-h@e�Y-�\��^�YO_�e`h=YIe"r�e`_�[=WEe�[\_�YOZ\e�_�YOa=r�moS-_`gCYIe�V8S-aqVXr�g�[�W�hCg�SU_�^�^;À/��^Qa=r�V8c-^U�U�=[/e(e�h=V8rVXr�f/^�WE^;�\e�V8c-^-��e�h=^�]"S-_�r�e�j�WQY-r�^qW;S-gq�\Z8^EÀ/Vbe��5SOm ')(+*-,/.10 VXr�Ð@[=YUf/_�YIe�VXWw®oV8aµ�\_`S-�+SUr�Vbe�V8S-a=Y-ZZ8S-T-VXWn^;c-^QaºZ8V8a\^QY-_�²E���\[/eqe`h=YIeCSOm ' 4 VXrq^EÀ/�+S-a\^QaUe`V8Y-Z{®o^;cU^;aºmoS-_q�\_`S-�+SUr�V}e`VbSUa=YOZ��\_`S-�\jZ8^;gCr`²EsC�wS-_`^;SIcU^;_ ' (+*-,-.�0 �\_`^Qr�^;_`c-^�r�e`h\^tr�e�_`[=W�e`[\_�^�SOm�e�h\^qmoSU_�g�[\ZXYnY-a=f5gCY��wZ8^QYUfke`Sg�[�W�hÅr�h\SU_�e`^;_ �\_`S@S-m�r;sq �azm�Y-WEe�V}e�VXr �\_`SIc-^QalV8a»v ¾Iy�e�h=YOe{e�h\^Q_�^q^EÀ/VXr�e�r{Ywr�^�Ð@[\^;a=W;^qSOmWEZXYO[�r�^{r�^Ee`r & � mo[\Zb�=ZbZ8V8a\Tqe�h\^ moSUZbZ8SI]�V8a\TCWES-a�f/V}e`VbSUa=rQ�$ ' (+*-,/.10 ® & � ²"h�Y-r�_`^Qr�S-Z8[/e�V8S-a�_�^;mo[/e`YOe�V8S-a=r�S-m�Z8^;a\T-e�h��°� N ��� �$ YOZ8Z�_`^Qr�S-Z8[/e�V8S-al_�^;mo[/e`YOe�V8S-a=r S-m ')4 ® & � ² Y-_�^qZ8S-a\TU^;_�e�h�YOa *U® ���¸|�²���]�h\^;_`^ *CVXr{Ya\SUa\^;Z8^;gq^;a@e�YO_`�qmo[\a=W�e`VbSUawf/^E�=a=^Qf��d�5*@®� U² � |�%*@® ���¸|�² � � � " � & s

��S-e�^�e�h=YOe *@® �²�T-_`SI]�r�m�YUr�e`^;_�e�h=Y-a�YOad���\À/^QftV}e`^;_�YIe�V8S-a�SOm3e�h=^�^;Àd�+S-a=^;a@e�VXYOZ�mo[\a=WEe�V8S-aKs��h\^�_�^�r�[\Zbe�YO�+SIc-^{VXr�SU�/e`Y-Vba=^Qf��d�n[�r�V8a\Tqe�h=^�WESUgq�\Zb^;À/V}e��nSOm(WE[/e�j�^QZbV8gqVba�YIe�V8S-aµ®�]�h\VXW�hVXr�a\SUa\^;Z8^;gq^QaUe�YO_`�\²�YOa=f�e`h\^�r�V8g�[\ZXYIe`VbSUawSOm�WE[\e�j�mo_�^Q^ �� ®RYOa=fwS-m �� ]�Vbe�h5Y-a=YOZ8�@e�VXWWE[\e�²�r�h\SI]�a�Vbane�h\^{a=^EÀde�r�[=�=r�^�W�e`VbSUaKs �a�vb|Q¾Oy=�(TUZb��Y-a=fq��YIe`h��\_`SIc-^�f{e`h=YIe�r�e�_`[=W�e`[\_�YOZ\WEZXYO[�r�^�moS-_`g·e�_�YOa�r�moSU_�gCYIe`VbSUa�VXr�a\S-e

S-a=Zb�Cr�[\��^Q_�V8S-_�Vbate�h\^QS-_`���=[/e�Y-Z8r�S�V8at�\_�Y-WEe�VXWE^-s���h\^Q��T@Y�c-^�Y{e�h\SU_�SU[\T-hC^;Àd�+^;_`V8g�^Qa@e`YOZWESUgq�=YO_`V8r�S-az]�Vbe�hÅe�h=^�r�e�YOa=f=YO_�f5e`_`Y-a=r�moS-_`gqYOe�V8S-aK� e`h\^Cc-^Q_`r�V8S-azSOm�e�h\^��\_�SIcU^;_ [=r�Vba=Tr�e�_`[=W�e`[\_`Y-Z@e�_�YOa=r�moS-_`gCYIe�V8S-a�f/V8f�a\S-e�SUa\Z8�{��^Qh=Y�c-^"��^;e�e`^;_�V8a�Y�cU^;_�YOT-^��\[/e(WESU[\Z8f�h=Y-a=f/Z8^�\_`S-�\Z8^;gCr"[\a=r�S-Z8cIYO�\Z8^�]�V}e`h�e`h\^{r�e�YOa=f\Y-_`ftc-^;_�r�VbSUaKsM��h=V8r�r�h\SI]�r�e�h=YOe�¨1¤��E¦E�;¤�©I�I����¥I¡z¥�È�b¥`ËO�����O�¦���¤�§=�E��§/¤���Vba�a\SU_�gCY-Z�moSU_�g WESUg��=[/e`YOe�V8S-a=r��=Y��/r"S-[\e�YOZXr�S�Vba��\_�Y-WEe�VXWE^Us�KA �KA��P *zL ���/FQPRH�D#H�� �� ��� ������H��RLF�P�H+D�A '°Vbe�h ')(+*-,/.10 ]"^�h�Y�c-^qYOa5SU��^Q_`YOe�SU_

]�h\VXW�hCf/Sd^Qr�a\S-e�SUa\Z8��gCYO�qY�moS-_`g�[\ZXY�Vba@e�S{Y r�^Ee�SOm3WEZXYO[=r�^QrM�\[\e�YOZXr�S ^;a�WES/f/^Qr�Y-ZbZ/S-m�Vbe`rr�[\�/moS-_`g�[=Z8YUr��d�qa\^;]°ZXYO�+^;ZXr�_�^Q�\_�^�r�^Qa@e�^Qfq�d�qa\^Q]¸�\_`^Qf/VXW;YOe�^�r��dg��+S-ZXr;s���h\VXr�gCY-i-^Qr�V}e�+SUr`r�V8�\Z8^qe�Swr�V8g�[=Z8YOe�^CV8a/mo^;_`^;a=W;^Qr V8a �� �@�5_�^�r�SUZb[/e`VbSUazf\^Qf/[=WEe�V8S-a=rQst%\SU_�r�V8gq�\Z8V8W;V}e��]"^�SUa\Zb�C�=_�^�r�^QaUe�e�h\^ �\_`S-�+SUr�Vbe�V8S-a=Y-Z�W;YUr�^U�@moS-_�e�h\^�mo[\Z8Z+�=_`r�e�j�S-_�f/^Q_�r�Vbg�[\Z8YOe�V8S-a�r�^Q^�vb|���yS-_�v ¾Iy�s �aºe`h\^��=_�r�etr�e�^;�»]"^�gCY-�»r�^QÐ@[\^QaUe�rqVba@e`SÅW;Z8Y-[=r�^QrQ¿�Y-ZbZ�]"^�h=Y�c-^ne�S¹f/SÅVXr�e�SÅ[=r�^

YIe`S-gqVXW�ZXYO�+^;ZXr�moS-_"moS-_`g�[\ZXY-r�Z8VbiU^�V8anr�e�_`[=W�e`[\_�YOZ3WEZXYO[=r�^�e`_`Y-a=r�moS-_`gqYOe�V8S-aKs��dSqY�r�^QÐ@[\^Qa@eSOmMe�h=^ moS-_`g

Π4 %�2 2�2 %�Π� � 9 4 %�2�2 2 % 9!�VXr�_�^Q�\_`^Qr�^;a@e�^�ft�d�te`h\^�WEZXYO[=r�^

�8)� % 2�2�2 % �8� � � � %�2 2�2 % � � 2��SI]¸Y-r`r�[\gq^�e�h=YOe�]"^�h=Y�cU^�Y�WE[\e�j�mo_�^Q^��\_`SdSOm �´S-m+e`h\^ r�^�ÐU[=^;a@e�Î � ®o]�h\VXW�ht�\_`SIc-^�r

e�h�YIe�Î V8r�[\a=r`YIe�VXr���YO�\Z8^�²Es���h\^Qa�]"^�WESUa=r�e�_`[=W�e ')(+*-,/.10 ®RÎ�²�s"��h\^�r�V8g�[=Z8YOe�V8S-a�SOm�ZbSUT-VXW;Y-Z

Page 17: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � |I�

V8aUe`_�S/f/[�W�e�V8S-a¹_`[\Z8^Qr�e�h\^QaµV8r���^Q_�moSU_�gq^�fÅc@VXYw_`^Qr�S-Z8[/e�V8S-aÅ[=r�V8a\Twe�h=^nWEZXYO[�r�^�r{^;a=W;S/f/Vba=Te�h=^Qr�^{Vba@e�_`S/f/[=WEe�V8S-a=rQs('z^�r�h\SI]Íe�h\^{�=_�S/WE^�f/[\_`^�moS-_�'º� �qYOa=f "º� �M]�h\VXW�hwr�[/ÁtW;^Qr�e`SV8ZbZ8[=r�e�_�YIe�^ e`h\^{a=YOe�[\_`^ SOme`h\VXr�e�_�YOa=r�moS-_`gCYIe`VbSUaKs�K^Ee�� 4 %���N �� j��\_`SdSOm�r�Y-a=f��z�+^�Y�r�[\�1f/^;_`V8c�YOe�V8S-a�SOm �°SOm�e�h\^ moSU_�g��

®��F4E²� 4+� �;4 ��� 4 % 9

®���N�²� NK����N ��� N�%�<

� Q ���+4 %���N ��� 4 % � N�%�9 '7< '´���

��SI]&Zb^;e � 4+��� 4 �� 4 % �°YOa�f � N�� N �� N�% �� �+^�e�h=^�WEZXYO[=r�^Qr�WESU_�_`^Qr���SUa=f/V8a\Te�S � 4 % � NOs(��r`r�[\gq^�V8a=f/[�W�e�V8c-^QZb�te�h=YOe�_�^�r�SUZb[/e`VbSUanf/^Q_�V8cIYIe`VbSUa=r ��4�S-m � 4�YOa�f ��N SOm � NYOZ8_`^QY-f\��^;ÀdVXr�eQs�'l^ WESUa=r�e�_`[=W�e�Y�_`^Qr�S-Z8[/e�V8S-atf/^Q_�V8cIYIe`VbSUaCSOm � �@e�h=^�W;Z8Y-[=r�^�_�^Q�\_�^�r�^Qa@e�V8a\T� Q s·u��Ãf/^;�=a\Vbe�V8S-a¸S-m ' (+*-,-.�0 ®�Î�²CY-a=f°�d�µe`h\^km�YUW�ete`h=YIene�h\^5moS-_`g�[\ZXY 9@' < V8rnYr�[\�/moS-_`g�[=Z8Y�SOm�Î$®oa=SOe�^�e`h=YIe�]"^�h�Y�c-^�e`h\^�r�[\�/moS-_`g�[=Z8Y��\_`S-�+^;_�e���P ² e`h\^�r�^Ee ' (/*-,/.�0 ®�Î�²WESUa@e`YOV8a=r"e`h\^�WEZXYO[=r�^Qr

� % � � �����¿ ����� � �¿ ����� � �� 2�r�V8a\Tqe�h\^�r�^{W;Z8Y-[=r�^�r�]�^{WQYOawWESUa=r�e`_�[�W�e�e�h\^ moSUZbZ8SI]�V8a\T�_`^Qr�S-Z8[/e`VbSUa�f/^Q_�V8cIYIe`VbSUa ��

® � N ²� N ��� N % �

® � 4 ²� 4 ��� 4 % % � � ����

� %�� 4 ��� 4 % ���� �

� N %�� 4 ��� 4 % � N % ���� �

]�h\VXW�h�V8r�Yq_`^Qr�S-Z8[/e�V8S-a�f/^;_`V8c�YOe�V8S-a�SOm�YqWEZXYO[=r�^ _�^Q�\_�^�r�^Qa@e�V8a\T � Q s��dS �wr�Vbg�[\ZXYIe�^�r���s��SI]¸]"^�V8ZbZ8[=r�e�_�YIe`^�e�h=^�WQY-r�^�SOme�h\^�a\^;T@YIe`VbSUaCVba@e�_`S/f/[=WEe�V8S-ate`S�e`h\^�Z8^Em«e�s(�K^;e��k�+^ Yr�[\�\�\_`SdSOm�S-m �°S-me`h\^ moS-_`g

®��KÏ«²� ÏQ��� ��� % 9� � " 9 %�� ���

"´���YOa�f �=Ï��+^�Y�_`^Qr�S-Z8[/e`VbSUa��=_�SdSOm3S-m3e�h\^�WEZXYO[=r�^ � ��� % _�^Q�\_�^�r�^Qa@e�V8a\T � ÏRs���r " 9 V8r�Yr�[\�/moS-_`g�[=Z8Y�S-m\δe`h\^�r�^Ee ' (/*-,/.�0 ®�Î�²WESUaUe�YOV8a=r1e`h\^�W;Z8Y-[=r�^�r � � % �� kY-a=f � % �� � su"[/e�e�h=^;a�e�h\^ moSUZbZ8SI]�V8a\Tq_�^�r�SUZb[/e`VbSUanf/^Q_�V8cIYIe`VbSUa �

® �+²� ��� % � � % �� �

�� %�� ��� �

�dVb^QZ8f=r�Y�_�^Q�\_�^�r�^Qa@e`YIe`VbSUa�S-m � s�dVbgqV8Z8Y-_Me�_�YOa=r�moS-_`gCYIe�V8S-a�rKW;Y-a���^�WESUa=r�e�_`[=W�e`^Qf moSU_e`h\^�S-e�h\^Q_MW;S-a\a=^QW�e`VbcU^QrMYOa=f�Vba/mo^Q_�j^;a�WE^QrQs�%MVba=Y-ZbZ8��]�^�SU�/e`Y-VbatY�_�^�r�SUZb[/e`VbSUatf/^;_`V8c�YOe�V8S-a���r�V8g�[\ZXYIe`Vba=T ��s���VXr"Y{_�^�r�SUZb[\e�V8S-af/^Q_�V8cIYIe�V8S-alSOm�e`h\^�W;Z8Y-[=r�^ �8 � s���h=^��=a=Y-Z�r�e`^;�5[�r�^�r�e`h\^CWEZXYO[=r�^ � �8¸]�h\V8W�hlV8r�V8a')(+*-,/.10 ®RÎ�²"�d��f/^E��a\V}e`VbSUawYOa=f�^;cU^;a@e�[�YOZ8Zb�C�dV8^;ZXf\r�e�h=^{_�^�r�SUZb[/e`VbSUa�_`^Emo[/e�YIe`VbSUa

®��d² �8 � � �8

� �

]�h\VXW�h�VXr�Y�_�^;mo[/e`YOe�V8S-a�S-m '5(/*-,/.�0 ®RÎ�² ��� ]�h\^Q_�^��ÍV8rMY�r�^Ee�SOm/e�YO[/e`S-Z8S-TUV8WQYOZUW;Z8Y-[=r�^QrKS-m/e�h\^moS-_`g 8 � 8 _�^Q�\_�^�r�^Qa@e�V8a\T{e�h=^�V8a\Vbe�VXYOZ3r�^�Ð@[\^;a@e`r�SOm ��s���S-e�^�e�h=YOe"^Qc-^;_`�q_�^�r�SUZb[\e�V8S-a_`^Emo[/e�YIe�V8S-a�W;Y-a���^�e�_�YOa=r�moS-_`gq^Qf{V8a@e�S�YOa\S-e�h\^Q_�®o^Qc-^Qa�r�h=S-_�e�^;_�²3SUa\^�]�h=V8W�h�VXre`YO[\e�S-Z8S-TU�@jmo_`^;^q®�r�^;^ ^-s T=s�v ¾- Iyo²�¿@e`h\^;_`^EmoSU_�^�]�^ W;Y-a�T-^;e"_`VXftSOme�h\^{r�^Ee��­Y-a=ft^Qc-^;a@e`[=YOZ8Zb�qSU�/e`Y-Vba�Y

Page 18: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

|Qx )1*O,/.1)+0123,/4k*-,/687+9;:=<_`^Emo[/e�YIe�V8S-a �dÏUSOm '5(/*-,/.�0 ®�Î�²YOZ8S-a\^Us��S-e�^�e`h=YIe�e�h\^�]�h\S-Z8^�r�Vbg�[\Z8YOe�V8S-a VXr1¨=¥I�¬¢I¡1¥I�����I�¬��e�h\^Z8^;a\T-e�h5S-m(e�h=^�_`^Qr�S-Z8[/e�V8S-a5�\_�SdS-m�®�W;S-[\a@e�V8a\T�e�h\^�ad[\g��+^;_ SOm�SdWQWE[\_`_`^;a=W;^Qr�S-m(moS-_`g�[=Z8YUrV8alYt�=_�SdSOm�²�VXr�Z8V8a\^QY-_�V8awe�h=^�Z8^;a\T-e�hlSOm�e�h=^ �� j��\_`SdSOm�¿+e�h=^�r��dg��+S-Z8V8W�Zb^Qa\TOe`h5W;Y-ak��^Ð@[=Y-f\_`YOe�VXW�f\[\^ e�S�e�h=^{Vba@e�_`S/f/[=WEe�V8S-a�SOm��di-SUZb^Qg e�^Q_�gCrQs'°V}e`h ' (/*-,/.�0 ]"^�W;Y-a�a=SOe�SUa\Z8��r�Vbg�[\Z8YOe�^�e`h\^�W;[/e�j�mo_�^Q^ �� �=[/e�YOZXr�S �� ]�Vbe�h��I¡1�I�¬¢I�����

WE[\eq®RYnW;[/e�VXr W;YOZ8Z8^QfkY-a=YOZ8�@e�VXW�Vbm(e�h\^qWE[\e�moS-_`g�[=Z8Y�SdWQWE[\_�r�Y-r�r�[\�/moSU_�g�[\ZXYtV8ake�h=^�^;a�fr�^QÐ@[\^;a@e�²�sk �a=f\^;^QfÅVbm VXr{e`h\^nW;[/e�moSU_�g�[\ZXY�Vba´Y-a¹Vba\mo^;_`^;a=W;^tSOm�YOa �� j��=_�SdSOm � SOmÎ � YOa�f�9·VXr�r�[\�\moS-_`g�[\ZXY�S-m�Î&]�^�h=Y�cU^�YOanYIe�SUg ��®���+²"YOa�fqe�h\^{f/^;�=a\V8a\T�moS-_`g�[\ZXYmoS-_�9q¿�e�hd[=r�e�h\^�WE[/e�]�V}e`h 9 W;Y-a¹��^�r�V8g�[\ZXYIe`^QfÅ�d�l_`^Qr�S-Z8[/e`VbSUaz]�Vbe�h ��® ���²�sw �m�]"^Y-f=f Y-_��\Vbe�_�YO_`�ºmoS-_`g�[\ZXY-r79 YOa�fÍWESUa=r�e�_`[=W�e ' (/*-,/.�0 ®:9�²�]"^ÅW;YOa ^;cU^;a¸�+S-Z8�da\S-gqVXYOZ8Zb�r�Vbg�[\Z8YOe�^�mo[\Z8Z �� sK��h\VXr r�e`_�SUa\T-^Q_�moSU_�g S-m�r�e�_`[=W�e`[\_`Y-ZMe�_�YOa=r�moS-_`gCYIe�V8S-a5V8r W;Y-ZbZ8^Qfke�h\^� -���;¡\¦���¥I¡ ¨1¤��«¡+�;� ¨+�b�;¿@V}e�]�Y-r�Vba@e�_`S/f/[=W;^Qf�®omoS-_M�=_�r�e�j�SU_`f\^;_Z8S-TUV8W�²K�d����s���f/^;_�vb|���y�s���hd[=r_`^Qr�S-Z8[/e�V8S-a � ^;Àde�^;a�r�V8S-akVXr�W;YO��YO�\Z8^�S-m�r�V8g�[\ZXYIe`Vba=T�cdVb_�e�[�YOZ8Zb��^;cU^;_`�nZ8S-TUV8W�W;YOZXWE[=Zb[=r�V8aYOan^QYUr��q]�Y��+�MS-a�WE^�]"^�h=Y�c-^�r�V8g�[\ZXYIe`^Qf �� ]"^�WQYOa�[�r�^{��^;a@e�pQ^;aK r�e�_�YOa=r�moS-_`gCYIe`VbSUa=rV8aÅvb|���y3e�Str�Vbg�[\ZXYIe�^ a=YOe�[\_�YOZKf\^Qf/[=WEe�V8S-a�YOa=f���VbZ8��^Q_�e�e��d�+^�W;Y-Z8W;[\ZbV�s

> � A�������H��RLF�P�H+D �����MD���*/�dD1F �UA ��r�_`^Qr�S-Z8[/e�V8S-a�VXr�YtWQYOZXWE[\Z8[=r�moS-_��\_�SdS-m�r�^QY-_`W�h�Y¹gCYOV8a°f/V8_�^�W�e�V8S-a°S-m�V8gq�\_`SIc-^;gq^QaUet]�Y-rw®Rr�V8a=W;^we�h\^5c-^;_`�´�+^;TUVba=a\Vba=T¹SOm{_�^�r�SUZb[\e�V8S-ae�h=^;S-_`^;g �=_�SIcdV8a\T@²�e�h\^�_`^Qf/[=WEe�V8S-azSOm��+SUr`r�Vb�\Z8^�_�^�r�SUZb[/e`VbSUa5f/^�f/[=W�e`VbSUa=r [\a=f\^;_ �\_`^Qr�^;_�jcIYIe`VbSUatSOmW;S-gq�\Z8^Ee�^Qa\^Qr`rQs���^Qa\^;_�YOZ8Zb��]"^�W;Y-ZbZ+YOad��_`^Qr�e�_`VXW�e�V8S-aCS-mK_�^�r�SUZb[\e�V8S-aCf/^Qf\[=W�e`VbSUaYä��E¦;¥I�¬§/����¥I¡ ¤���Æ�¡+�;�q�;¡=��s ��^Qr�e�_`V8WEe�V8S-a=rCS-m�e`h\^k_`^Qr�S-Z8[/e�V8S-a»�\_`Vba�WEV8�\Zb^lf/V8fÃa=SOetS-a=Zb�V8g��=_�SIcU^qe�h\^n^EÁtWEV8^;a=W;�lS-m�e�h\^QS-_`^;g �=_�SIcU^;_�r �\[/e�Y-Z8r�SwZ8^QY-fze`Swe�h=^�f/^;cU^;Z8S-�\gq^QaUe�SOmZ8S-T-VXW��\_�SUT-_�YOgqgqVba=TnYOa�flf/^�WEVXr�V8S-al�\_`SdW;^Qf/[=_�^�r;¿3e`h\^CZXYIe�e`^;_{YO�=�\ZbVXW;YOe�V8S-aÅYO_`^QY�]�VbZ8Z���^e�_`^QYOe�^�fÅVbaµ�d^�W�e�V8S-a´~\s� �a¹gCYOad�5Y-�\�\Z8V8WQYIe`VbSUa=r{SOm�_`^Qr�S-Z8[/e�V8S-az]"^tYO_`^Ca\SOe�V8a@e�^;_`^Qr�e�^�fV8a�e�h\^�f/^�f/[=WEe�V8S-a=r�e`h\^;gCr�^;Z8c-^�r��\[/e�_�YIe`h\^;_�V8a�e�h\^�f/^Qf/[�W�e�V8c-^�W;ZbS@r�[=_�^C®oV�s ^-s�V8a�e�h\^�r�^;eSOm�f/^Q_�V8cIYO�\Z8^tWEZXYO[�r�^�r`²Esn��h\VXr�YUr��+^QWEe�SOm�f/^Qf\[=W�e`VbSUa¹V8r���^�r�e�f\^Qr`WE_`Vb�+^Qfz�d�´¤��E¦;¥I�¬§/����¥I¡¥`¨=�;¤��I��¥I¤�¦�s� ����������������� �=s8|�®�_�^�r�SUZb[/e`VbSUanSU��^Q_`YOe�SU_�² ���K^;e &º�+^tYwr�^;e�SOm"W;Z8Y-[=r�^Qr{YOa�f �l�E¦U® &K²

f/^Qa\SOe`^�e�h\^�r�^Ee(SOm1YOZ8Z/_�^�r�SUZbcU^;a@e`r�f/^;�=a=Y-�\Zb^"mo_`S-g &�YOa=f�r�[=�/��^QWEe�^Qf�e`S Y�a\SU_�gCY-ZbV8pQYOe�V8S-a[\a=f\^;_CY5r�e`Y-a=f\YO_�f¹_`^;a=Y-gqVba\TlSOm�cIYO_`VXYO�\Z8^QrQsz��h=^;a´]"^�f/^E�=a=^�e`h\^nSU��^Q_`YOe�SU_ ����e�h\^¥`¨=�;¤��I��¥I¤�¥�È{§/¡=¤`��¦���¤����E����Êq¤��E¦E¥O�¬§/����¥I¡tYOa�f�Vbe`r�f\^Qf/[=WEe�V8c-^�W;ZbS@r�[\_`^�� � �d�

�q® &² � & � �l��¦@® &²?% � 4 ® &² � &;%� ) � 4 ® &² � �q® � ) ® &K²�²?% � � ® &² � 2

)�� 6 0� ) ® &²?2 �

��SOe`^ e�h=YOeQ�\�d��e�h\^�W;S-gq�\Z8^Ee�^Qa\^Qr`r�SOmMe�h=^{_�^�r�SUZb[/e`VbSUan�=_�V8a=WEV8�\Z8^-�/]"^{h=Y�c-^ � � � � ® &K²moS-_�[\a=r`YIe�VXr���YO�\Z8^tr�^Ee`r�SOm�WEZXYO[=r�^Qr &�s�u��le�h=^C[\a=f/^�WEVXf\YO�\V8Z8V}e��zSOm�WEZXYO[=r�^CZ8S-T-VXW � � ® &K²g�[�r�e��+^{Vba\�=a\Vbe�^ moS-_�r�SUg�^{r`YIe`V8r���YO�=Zb^ r�^;e`r�S-mMW;Z8Y-[=r�^�r#&�s��^E�=a=^;gq^;a@e�S-�+^;_�YIe�SU_`r�W;YOa���^�f/^E�=a=^QftV8a�Y�r�V8gqVbZXYO_�]"Y��1¿@]�^�S-a\Z8�qh=Y�c-^�e`S�_`^;�\ZXY-W;^

�l�E¦ �d��YOa\S-e�h\^Q_"SU��^Q_`YOe�SU_Qs� ����������������� �=s �5®�_�^;�=a\^;gq^QaUe�SU��^Q_`YOe�SU_�² ��� ¤��E¦E¥O�¬§/����¥I¡¸¤��RÆ(¡1�E�C�;¡=��¥`¨=�;¤��I��¥I¤ � %

VXr�Y�gCY-�\�\V8a\T�mo_`S-g�r�^;e`r"SOm�WEZXYO[=r�^Qr�e�Sqr�^Ee`r�S-mMW;Z8Y-[=r�^�r�f/^E�=a=^QfnVbane�h\^�moSUZbZ8SI]�Vba=T�]�Y��1���h\^Q_�^ ^EÀ/VXr�e�r�Y�®oSUa\^Ej�r�e`^;��²�SU��^Q_`YOe�S-_�� % r;s eQs$ � % ® &² � & ��� % ® &²��$ � % VXr�_`^QWE[=_`r�VbcU^-�$ � % ® &²"VXr�Y��=a\Vbe�^�r�[\�=r�^Ee�SOm � � ® &K²Es

Page 19: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � |�¶

��T@YOV8a�e�h\^�f/^�f/[=WEe�V8c-^{WEZ8SUr�[\_`^�VXr�f/^;�=a\^Qf�YUr� 4% ® &² � &5% � ) � 4% ® &² � � % ® � )% ® &²�²3%� �% ® &² � 2

)�� 6 0� )% ® &²?2 �

��h\^q_�^�ÐU[=Vb_`^;gq^;a@e � % ® &²� � � ® &²��KV8a=r�e�^QYUf5S-m�� % ® &² �l�E¦U® &K²E�r�^;_`c-^Qr�e�h=^��=[\_�j�+SUr�^ e�Sq^;a=W;S-gq�=YUr�r"gq^Ee`h\S/f\r�SOm�gCY-W;_�S-j�V8a/mo^;_`^;a�WE^�®Rr�^Qc-^Q_`Y-Z3_�^�r�SUZb[/e`VbSUanr�e�^Q�=r�gCY��t��^WESUa=r�V8f/^Q_�^�f�YUr��=_�V8gqV}e`VbcU^�V8a/mo^;_`^;a�WE^�r�e`^;��²Es��/[=W�h�Y��\_`Vba=W;Vb�=Zb^"V8r�hd�d�+^;_`_�^�r�SUZb[/e`VbSUa�]�h\VXW�h]�V8ZbZ��+^�f\^Qr`WE_`Vb�+^Qf5Vba5e�h\VXr r�^�W�e�V8S-as���SOe{YOZ8Z�_�^;�=a\^Qg�^Qa@e`r W;Y-ak��^�moSU_�g�[\Z8YOe�^�fw]�V}e`h\V8ae�h=^�mo_�YOgq^;]"S-_`i{SOm3S-�+^;_�YIe`S-_�r;¿-Vba=f\^;^QfqZ8V8a\^QY-_(_�^;�=a\^Qg�^Qa@e`r�Y-_�^�f/^;�=a\^�fCcdV8Y�e`h\^�_`^Qr�e�_`V8WEje�V8S-a�S-m�e`h\^�_`^Qr�S-Z8[/e�V8S-a�e�_`^;^-�=]�h\V8W�hwWQYOa\a\S-e���^{moSU_�gCY-ZbV8p;^�f��d�tSU��^Q_`YOe�S-_�r ®«moSU_�f/^Ee�YOV8Z8rr�^;^tv ¾- Iyo²�s� AR?�A � GIJ��@G�PRD � �����MD���*/�dD1F �UA ��h\^q[=r�^CSOm�S-_�f/^;_`Vba=Tn_`^E�=a=^;gq^;a@e`r VXr{�=YUr�^�f5SUa

e�h=^�VXf/^QY�e�Sni-^Q^;�5_`^Qr�S-Z8c-^Qa@e`rC¯`r�gCYOZ8ZX±\s ��h\V8r f/Sd^�r�a\S-e�SUa\Z8��Z8^QYUf�e�S�r�gqY-ZbZ8^;_ WEZXYO[�r�^�rf/[\_`V8a\T�f/^�f/[=W�e`VbSUa��\[/e�YOZXr�S�e�S�Y-a{Vbgq�\_`SIc-^�f�e�^;_`gqVba�YIe�V8S-a{�+^;h�Y�c@V8S-_SOm/S-�+^;_�YIe`S-_�r;s��h=^gqSUr�e"W;S-gqgqS-atSU_`f/^Q_�V8a\T{�\_`V8a=WEV8�\Z8^�SOm3e`h\VXr(e��d�+^�VXr��O��¥O�$¥I¤�ÊU�E¤��«¡dËO¿/V8aCe�h=V8r"_`^Qr�e�_`V8WEe�V8S-aa\S�_`^Qr�S-Z8c-^Qa@e`r(Y-_�^�YUf/gqV}e�e�^Qfq]�h=V8W�htW;S-a@e`Y-VbatYOe�S-gCr�gqSU_�^�W;S-gq�\Z8^EÀ�e�h=Y-aCe�h\^�_�^�r�SUZbcU^QfS-a=^-s� ����������������� �=s ¾�����aÍ��j�S-_�f/^Q_�V8a\T¸®�YOe�SUg SU_`f/^Q_�V8a\Td²�� VXr�Yµ�\Vba�YO_`�º_`^;ZXYIe`VbSUa»SUa

YIe`S-gCr�]�Vbe�h�e�h\^ moSUZbZ8SI]�V8a\Tq�\_�SU��^Q_�e`Vb^�r;���sb|��ÍVXr�V8_�_`^ �=^;À/VbcU^-���s ���ÍVXr"e�_�YOa�r�Vbe�V8c-^U���s ¾Ã%\SU_�YOZ8ZKYIe`S-gCr %OB YOa=f�moS-_�Y-ZbZr�[\�=r�e�Vbe�[\e�V8S-a=r �\� �� BÉV8g��=ZbV8^Qr ��� B �\s ���h\^��\_`S-�+^;_�e�����s ¾�TU[=YO_�YOa@e`^;^Qre�h=^�ZbVbm«e�V8a\T �\_`S-�+^;_�e��{moS-_���j�S-_�f/^Q_�V8a\TUrM]�h\VXW�h�V8r�cdVbe`YOZ

e�StW;S-gq�\Z8^Ee`^;a\^�r�rQs������������� �=s8|����K^;e YOa=f BÄ��^�e�]"SzY-_��=V}e`_`Y-_��µYOe�S-gCrQsº'z^wf/^E��a\^�e�h\^´ÊU��¨1�«�

¥I¤`Ê-�;¤��«¡@Ë���{�@� ��� B VbÇ

fK|-s �K®� �² ���K®0B�²?%f��/s=cIY-_Q® �² ´cIY-_�®�B�²�YOa�f��� ���/®$�&% �² � �� ���\®$�&%JB�²�moS-_ ����cIYO_Q®� �²32

]�h\^Q_�^��kV8r�e`h\^�e`^;_`g f/^;�/e`hlY-a=f � ��� ®$��% �²�e�h\^�gCYIÀ/V8gqY-ZMf\^;�/e`h5SOm�e`h\^�c�Y-_�VXYO�=Zb^ �V8a �s �eqVXr�^QYUr��ze�SÅr�^;^ne�h=YOe�e`h\^wf/^;�/e`h´SU_`f/^Q_�V8a\T�� � mo[=Z}�=ZXrC��s8|-� ��s �/� ��s ¾zYOa=fµe�hd[=r�V8r

V8a=f/^;^�flY-a5��j�S-_�f/^Q_�V8a\T=s ��S-e�^�e�h=YOe��d�kW;S-a=f/Vbe�V8S-azf3|-s{Y-ZbSUa\^�e`h\V8r ]"S-[=Z8fwa=SOe ��^�e�h\^W;YUr�^U���r`r�[\gq^�e�h�YIe "C®$�1²�� � "C®HK�®0M/²�²Es(��h\^;a��d�t��s ¾�®�[=r�Vba\T � � �54/K�®�Md² ��²�]�^ h=Y�cU^

"C®$�1² ��� � "C®HK�®0M/²�² �\�3VRs ^-s "C®�K�®�M/²�²�� � "C®�K�®�M/²�²�s u"[/e�e`h\^�Z8YUr�e�_�^QZ8YOe�V8S-akWESUa@e�_�Y-f/VXW�e�r��s8|-s���^Qa\^;_�YOZ8Z8�� �� B­VXr�V8g��+SUr`r�Vb�\Z8^ moS-_�[=a\V}�+YO�\Z8^{YIe�SUgCr ·YOa=fIBts�dS-gq^ mo[\_�e�h\^Q_�^EÀ\YOgq�\Z8^Qr"moSU_�e�h\^���;j�_�^QZ8YOe�V8S-aK�

"C®$�&%# \²��� "C®HK�®$�1²?%OK�®0 \²�²���"C®$�&%#�+²��� .C® �3®$�&%# \²�²E�.C®0�+² ��� .t®�K�®0M/²�²���f=�\s�V8r�cdV8S-ZXYIe`^Qf3�.C®HK�®0M/²�² ����.C®$�1²���f3|Us�V8r�cdV8S-ZXYIe`^Qf3s ���a\S-e�h\^Q_ �j�S-_�f/^;_`Vba=T�]�h\VXW�h�]�V8Z8Z/e�[\_`a�S-[/e�[=r�^Emo[\Z/V8a�e�h\^�a\^;Àde�r�^QWEe�V8S-a�V8r�W;S-gq�=YO_`V8a\T

_�YIe�h=^;_�e�h=^�r�V8p;^�e�h�YOa�e�h\^�f\^;�/e`h�S-m�e`^;_`gCr;s

Page 20: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

�O  )1*O,/.1)+0123,/4k*-,/687+9;:=<������������� �=s ���'z^�f/^E�=a=^ Y-a�S-_�f/^;_`Vba=T��d�C�=_�r�e�W;S-gq�=Y-_�V8a\T�mo[\a=W�e`VbSUa=YOZKe�^;_`gCr;�

e�]"S�mo[\a=WEe�V8S-a=Y-Z-e`^;_`gqr�YO_`^(W;Y-ZbZ8^Qf�¦��«���«�b�I¤KVbm *�� �3® � 4 %�2 2�2�% � �\²KY-a=f � �=K�®�� 4 %�2 2�2�%����\²YOa�f � 4 % 2�2�2 % � ����� �� 4 % 2�2 2 %�� ���Us(�dV8gqVbZXYO_�e�^Q_�gCr�gqY��qh=Y�cU^�f/VbÇ+^Q_�^Qa@e�e�SU��r��@g���SUZ8r�\[/e�e�h\^QVb_�Y-_�TU[\gq^;a@e`r�YO_`^ ^QÐ@[=Y-Z3[\a=f/^Q_���^Q_�g�[/e`YOe�V8S-a=rQs�°mo[\a=WEe�V8S-a=Y-Z/e�^Q_�g *�Ê-¥I���«¡+�O���E¦(Y�mo[\a=WEe�V8S-a=Y-Z\e�^Q_�g ��V}m ��h=YUr�Zb^�r�r�YO_`T-[\gq^;a@e�r�e�h=Y-a

*{SU_�gqS-_`^�moSU_�gCYOZ8Z8�$ *��=K�® � 4 % 2�2�2 % � � ²E� � � �3®���4 % 2�2 2 %�� � ²��$ ��� � �$ ���4 %�2�2 2 %�� � �� � 4 % 2�2 2 % � � �Us��h\^�WES-a�WE^;�\e`r�YO�+SIc-^�WQYOa���^�[=r�^Qf�Vbaqf/^E��a\Vba=T�e`h\^"e�^;_`g·S-_�f/^Q_�V8a\T ��4��O]�h\^;_`^ * ��4 �

VbÇ$ * �\_`S-�+^;_`Z8�tS/W;WE[=_`r"V8a �"S-_$ ��f\S-gqVba�YIe�^�r*{SU_$ ��W;S-a@e`Y-Vba�r�Y��=_�SU��^Q_�r�[\�\e�^;_`g ]�h\VXW�hwf/S-gqV8a=YIe`^Qr* SU_�V8r�r�V8gqVbZXYO_"e�S *Us�dS-gq^{^EÀ\Y-g��=Zb^�r"moS-_ � 4 �

K�®$�&%# \²�� 4� ®$�&%# F%J1d²��Me�h=^�r�^�WES-a�fte`^;_`g�f/SUg�V8a=YOe�^Qr"e`h\^ �=_�r�e�SUa\^-sK�®$�&%# \² �� 4 �3®$�&%# \²���e`h\^ e�^Q_�gCr�YO_`^{r�V8gqVbZXYO_�s�3®$ F%#�1² ��4�3®�K�®$�&%# \²?%J�+²E�ne`h\^kr�^QWESUa=f¹e`^;_`g WESUa@e`YOV8a=rqYz�\_`S-�+^;_Cr�[=�/e�^Q_�g ]�h=V8W�h»V8rr�VbgqV8Z8Y-_�e�Sqe�h=^ �=_`r�e�e�^Q_�g�s��h\^{SU_`f/^Q_�V8a\T���4�W;Y-an^�Y-r�VbZ8�C��^{^;Àde�^;a�f/^Qfne�StY-a�YOe�SUg S-_�f/^;_`V8a\T � N{f\^E�=a\^�f��@�1� � N B�Vbǹe�h=^;_`^�^;ÀdVXr�e`r YOazYO_`T-[\gq^;a@e ��SOm B�r�[=W�hke`h=YIe moSU_ Y-ZbZ�Y-_�TU[\gq^;a@e`r *�SOm ]"^{h=Y�c-^!* ��4 ��s�dS-gq^{^EÀ\Y-g��=Zb^�r"moS-_ � NO�

"C®$�&%# \²�� N .C®HK�®$�&%# \²�²E���@�>� ��4 K�®$�&%# \²�YOa=fR ��4 K�®0��%J /²Es"C®$�&%J1d² �� N .C®�K�®0��%J /²�²��(�d�>1 ���4 K�®0��%J /²Es �'l^�f\^E�=a\^�e�h\^���j�SU_`f/^Q_�V8a\Tq_`^E�=a\^Qgq^;a@e�cdV8Y ���® &²E�=]�h\VXW�hwf/^Qr`WE_`Vb�+^Qr�e�h\^�r�^Ee�S-m�Y-ZbZ

��j�_�^�r�SUZbcU^;a@e`r�Vba &�s°��h\^Ť��E¦E¥O�¬©I�`ʺ�I��¥I� S-m�Yz_`^Qr�S-Z8[/e�V8S-a»V8r�e`h\^kYIe`S-g W;[/etS-[\eq�d�_`^Qr�S-Z8[/e�V8S-aÅ®�YOm«e�^;_�Y-�\�\Z8V8WQYIe`VbSUanS-m�e`h\^{g�s T�s [Ks r�²�s� ����������������� �=s �z®�S-_�f/^;_`^Qf�_�^�r�SUZb[/e`VbSUa�²����K^;e &´��^tY�r�^Ee�SOm�WEZXYO[=r�^Qr Y-a=f � ��^tY-a

��j�S-_�f/^Q_�V8a\T=sº'l^kf\^E�=a\^ � � � ® &²�V}Ç � � �l�E¦U® &K²�Y-a=fµmoSU_Ca\S¹YIe`S-g B V8a � � � Bt�\]�h\^Q_�^ &VXr�e�h=^{_�^�r�SUZbcU^Qf�YOe�SUg SOm�e�h\^�W;S-_`_�^�r��+S-a=f\Vba\T�_`^Qr�S-Z8[/e�V8S-aKs���;�C�I¤)(�� ��^E�=a\Vbe�V8S-a5�=s ��_`^Qr�e�_`V8WEe`r�_�^�r�SUZbcU^;a@e`r(Vba�Y�]�Y���e`h=YIe�S-a=Zb�qgCYIÀ/V8gqY-Z+YOe�SUgqr�V8aYqWEZXYO[=r�^�gqY�����^ _`^Qr�S-Z8c-^QfKsMu"[/e�a\S-e�^�e�h�YIe�e�h\^{SU_`f\^;_`Vba\T�h=Y-r"e`S��+^�WESUa=r�V8f/^Q_�^�f�YOm«e�^;_YO�=�\ZbVXW;YOe�V8S-a�SOmMe�h=^�g�s T�s [Ks�®«e�h=V8r�S-_�f/^;_`Vba=T��=_�V8a=WEV8�\Z8^{V8r�W;YOZ8Z8^Qf¹�`¨=¥�¦����E¤���¥O¤��"¥I¤`Ê-�;¤��«¡@Ë�²�s

�������������� �=s ¾����K^;e �� ��^ e`h\^{S-_�f/^Q_�V8a\T�mo_�SUg$��À\YOgq�\Z8^ �=s8|{YOa=f

& � � "C®0M/²�¿ "C®0�+² � �q®�K�®0�+²�²E¿ �q®$ \² � ��®HK�®$ \²�²E¿ �q®�K N ®�M/²�² � ��2��h\^Qa

� � ® &²/�,& �+ �q®�K�®�M/²�² � % "C®�K�®�M/²�² � ��%� N � ® &²/���� � ® &²��+ �q®0M/² � % "C®0M/² � ��%� Q � ® &²/��� � � ® &² � �

N � ® &²�� � � 2

Page 21: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � �\|

��S-e�^we`h=YIene�h\^Q_�^lYO_`^wg�SU_�^kW;Z8Y-[=r�^QrCV8a � � ® &K²Es ��s T=s � �q®HK�®0M/²�² � �l��¦U® &²����\[/eh\^Q_�^ "C®�Md²�V8r�e�h\^{_`^Qr�S-Z8c-^�fnYOe�S-g YOa=f "C®�M/²��� �q®HK�®0M/²�²E�\e�hd[=r � �q®�K�®0M/²�² �� �� � ® &²�s�dV8gqVbZXYO_`Zb� "C®$� 4 ² � �q®�K N ®$� 4 ²�² � �l�E¦U® &K² � � � ® &²��IY-rKe�h\^�_�^�r�SUZbcU^Qf�YIe�SUg VXr �q®HK�®$� 4 ²�²YOa�f �q®HK�®$�F4;²�²�� � ��®HK N ®0�F4Q²�²�s �� SI]"Y-Z8r�idV@Y-a=f���Y��-^Qr�h=Y�cU^�r�h\SI]�a�V8anv �OxOy@e`h=YIe�� VXr�WESUg��=Zb^;e�^�moS-_�YOad�{��j�S-_�f/^;_`V8a\T

�{�V�s ^-s � ��� � ® &²�]�h=^;a\^Qc-^;_ &ºV8r{[=a=r�YOe�VXr��+YO�\Z8^-sq'z^C]�VbZ8Z�r�h\SI] V8aµ�d^QWEe�V8S-a¹~te`h=YIeWESUgq�\Zb^;e�^Qa\^Qr`rtYOa�f´TUS@S/f´e�^Q_�gqV8a=YIe`VbSUa»�=_�SU��^Q_�e`Vb^�rqgqY-i-^�S-_�f/^Q_�V8a\Tz_�^;�=a\^;gq^QaUe�r�e�h\^VXf/^QY-Z3e�SdS-Z1moSU_�_�^�r�SUZb[\e�V8S-a�f/^QW;V8r�VbSUan�=_�S/WE^�f/[\_`^QrQs� A �3A�� � � �@G�G.� ��H���L�FQP�H+D�A '°h\V8Zb^(SU_`f\^;_`^Qf�_�^�r�SUZb[/e`VbSUa�[�r�^�r1e�h\^�WES-gq�\Z8^EÀ/Vbe���S-mdYOe�S-gCr

e�S5_�^�r�e`_�VXW�e�_`^Qr�S-Z8[/e`VbSUaK�hd�d��^Q_�_`^Qr�S-Z8[/e`VbSUazW;S-a=W;^;a@e�_�YIe`^Qr{SUale`h\^nr�V8T-aÅSOm�WEZXYO[�r�^�r;s�'l^W;Y-ZbZ�YkW;Z8Y-[=r�^t¨\¥I¦��«�R�«©I��V}m�Vbe�VXr�SOm�e�h=^tmoS-_`g � 4 %�2 2�2�% � sl��S-[\TUh\Zb�År���^�YOidVba=Tkhd�Uj�+^;_`_�^�r�SUZb[/e`VbSUa�V8r�e�h\^�f\^Qf/[=WEe�V8S-aw�\_`V8a=WEV8�\Z8^�]�h\^;_`^�SUa\Zb�n��S@r�Vbe�V8c-^�WEZXYO[=r�^Qr�®RYOa=f � ²�YO_`^f/^Q_�V8cIYO�\Z8^-¿�e�h\VXr�VXr�S-a\Z8�l�+SUr`r�Vb�\Z8^�Vbm�SUa\^Ej�r�e`^;�¹_`^Qr�S-Z8[/e�V8S-a¹VXr�_�^Q�\Z8YUWE^�fÅ�@�ÅgCYOad�@j�r�e`^;�V8a/mo^;_`^;a=W;^QrQs(��h\^ moS-Z8Z8SI]�Vba\T�^EÀ\Y-g��=Zb^ gqSOe`VbcIYIe`^Qr�e`h\VXr��\_`Vba=W;Vb�=Zb^ SOm�gCY-W;_�S-j�V8a/mo^;_`^;a�WE^-�������������� �=s �����K^;e &l�+^ e�h\^�r�^Ee�SOm�WEZXYO[�r�^�r � 4 % � N % � Q % � � � moS-_

� 4 � � "C®0M�% >E²?% � N � � "C®?> %JM/²?% � Q � "C®$�&%# \²?%O"C®$ F%J1d² � "C®0��%O1@²3% � � � "C®�M�%JM/² � � 2��h\^Qa�V8ate�h=^�moSUZbZ8SI]�Vba=T�_�^�r�SUZb[\e�V8S-at_`^Emo[/e�YIe`VbSUatS-a\^�SOmKe`h\^�_�^�r�SUZbcdV8a\T�WEZXYO[�r�^�r(VXr"Y-Zb]�Y��/r�+SUr�V}e`VbcU^-�

� "C®�M�% >E²� "C®:> %OMd² "C®0��%J /²3%J"C®0 �%O1@² � "C®0��%J1d²

"C®$�&%�>E² � "C®$�&%JM/² �

� "C®0M�%OMd² � "C®0M�%OMd² �� �

��h\^tW;Z8Y-[=r�^ "C®$�&%�>E² � "C®0��%JM/² WQYOaz��^qV8aUe`^;_`�\_`^Ee�^�flY-alV8a@e�^Q_�gq^Qf\V8Y-_���_`^Qr�[\Z}e{Z8^QYUf/Vba=Te�S�e`h\^{WEZXYO[=r�^ � "C®0M�%OMd²Es��dS�]�^{r`Y���e`h=YIe � "C®0M�%OMd²�VXr�Yq�/¢`¨\�;¤�¤��E¦E¥O�¬©I�E¡��KSOmKe`h\^{WEZXY-r�hr�^QÐ@[\^;a�WE^k® � Q ¿ � 4 % � NQ²Esn �aze�h=V8r�r�^Qa=r�^�e`h\^tS-a=Zb� ¯�gCY-W;_�S-j�_`^Qr�S-Z8c-^QaUe�r�±�YO_`^ � "C®�M�%OM/²YOa�f � s(��SOe`^�e�h=YOe � Q gCY��ta=SOe��+^{_�^�r�SUZbcU^Qft]�Vbe�h ��� Y-r�a=S-a\^ SOmMe�h=^;g$VXr��+SUr�V}e`VbcU^-s� ����������������� �=s ~���^Ee � �+^�Y�a\SUa\��S@r�Vbe�V8c-^CW;Z8Y-[=r�^tY-a=f�� 4 %�2 2�2�%�� � �+^t�+SUr�V}e`VbcU^

WEZXYO[�r�^�r;¿�e`h\^;a � �M® � ¿�� 4 % 2�2 2 %�� � ²{VXr�WQYOZ8Zb^�f¹YkWEZXY-r�h´r�^QÐ@[\^Qa=WE^Us5�K^;e � 4 � � Y-a=f�*) � 4 � �l�E¦@® �*) %�� ) � 4 ��²�moS-_ + � |�% 2�2 2 %�� �»|Us( �m � � VXr�f/^;�=a\^�fwYOa=f��+SUr�V}e`VbcU^ e�h\^QaVbe�VXr W;YOZ8Z8^QfkY��d¢`¨=�E¤�¤��E¦;¥I�¬©I�;¡=��SOm � s 'l^qf/^E��a\^�e`h\^�r�^Ee SOm"YOZ8Z�hd�d��^Q_�_`^Qr�S-Z8c-^Qa@e`r�mo_`S-gYqr�^;e�SOmMW;Z8Y-[=r�^Qr &lY-r � ��® &²�s(��h\^{WESU_�_`^Qr��+S-a=f/V8a\T�_�^�r�SUZb[\e�V8S-a�SU��^Q_`YOe�SU_ � �&V8r�WQYOZ8Zb^�fe�h=^{S-�+^;_�YIe�SU_�SOm�h@�d�+^;_`_�^�r�SUZb[\e�V8S-aKs���;�C�I¤)(��t��h\^tSU��^Q_`YOe�SU_ � � �\ZXY��dr�YOa¹V8gq��SU_�e�YOa@e�_`S-Z8^tVba´ZbSUT-VXWq�\_�SUT-_�YOgqgqVba=T=s� �a�=Y-_�e`V8W;[\Z8Y-_ � � WESUVba=W;V8f\^Qrn]�V}e`h¸e�h=^lSU��^Q_`YOe�S-_�� ®0"³�+^;V8a\T»Y´Z8S-TUV8Ww�=_�SUT-_�YOgt²qV8a��SU_�anZbSUT-VXWO¿���µf/^;�=a\^Qr�e`h\^ Zb^�Y-r�e��\À/^�ft�+S-V8aUe�S-m�Y�Z8S-TUV8W��\_`S-T-_�YOgÉV8a�e`h\^�f\^QWEZXYO_�YIe`VbcU^r�^;gCYOa@e�VXW;r{v ¾\|;y�s ����d��^Q_�_`^Qr�S-Z8[/e`VbSUa�]�Y-r"r�h\SI]�anWES-gq�\Z8^Ee`^��d� ��s ��s\��S-�=Vba=r�S-a�VbaÅv ¾UÌIy�s���h\^�W;S-a=r�e�_`[=WEj

e�V8S-a�SOm\hd�d��^Q_�_`^Qr�S-Z8c-^Qa@e`r3W;Y-a��+^"r�[\�/��^�W�e�^�f e�S�cIYO_`VbSU[=rYUf\f/Vbe�V8S-a=Y-Z-_`^Qr�e�_`V8WEe�V8S-a=rQ��ZbV8i-^(_`^Ejr�e�_`V8WEe�V8S-a�SOm=m�YUW�e`S-_`Vba\T�e�S �+SUr�V}e`VbcU^�WEZXYO[=r�^Qr�YOa�f�r�e�_`V8WEe�S-_�f/^;_`Vba=T�SOm+a\S-a=��S@r�Vbe�V8c-^�WEZXYO[�r�^�r®�r�^;^tv ¾- Oy«²Es �m�]�^ke`YOiU^!& Y-r�VbaÍ�(À\YOgq�\Z8^ �=s �¹e�h=^;a � �� ® &² � &�� � "C®0M�%OMd²3% � �zYOa=f¸Y-ZbZ

�\_`S/f/[=WE^�fqWEZXYO[=r�^Qr�WESUa@e`YOV8aqYIe�gqSUr�e�SUa\^�YIe`S-g�s� �a�f/^;^�f3�-SUa� �¥I¤�¡��8¥�Ë-���E� � � �\_�S/f/[�WE^QrS-a=Zb���+SUr�V}e`VbcU^�[\a\Vbe W;Z8Y-[=r�^Qr�Y-a=fµ®o�+SUr`r�Vb�\Z8�\² � ®RY�WEZXYO[�r�^�VXr���S-_`awVbm(V}e�V8r�SOm�e`h\^�moSU_�g

Page 22: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

�-� )1*O,/.1)+0123,/4k*-,/687+9;:=< 4 %�2 2�2 % � � S-_ 4 %�2�2 2 % �� � B­moS-_ � �¸ U²�s���awr�YOe�VXr��+YO�\Z8^�r�^;e`r�SOm���S-_`akWEZXYO[�r�^�r� � WQYOaµ�+^�Vba@e�^Q_��=_�^;e�^Qf¹YUr�Y´�q¥�Ê-�;��ªE§/�«�8Ê-�;¤(�� �m � � ® &² �%&°Y-a=f � �� &»e`h\^;a´e�h\^�+SUr�V}e`VbcU^5WEZXYO[=r�^QrtVba � � ® &²q_�^Q�\_`^Qr�^;a@e�Y°®ogqV8a\VbgCY-ZX²���^;_`�\_�YOa=f»gqS/f/^;Z�SOm &É®omoS-_�Y�\_`SdSOmMr�^;^{^Us T�s�v ¾U Iyo²�s������������� �=s ~���K^;e

& � � "C®�M/²�¿ "C®$�1² � "C®�K�®0�+²�²E¿ "C®:>E² � � 2��h\^Qa�&lV8r�r`YIe`V8r���Y-�\Zb^{Y-a=f

� �� ® &²/�,& �+ � "C®�K � ®�Md²�²�6 � � | � 2��S-e�^ e`h=YIe � �� ® &²"V8r�Y��\À/^Qf��+S-V8a@e�SOme`h\^{S-�+^;_�YIe`S-_ � � YOa=f � �� � �� ® &²Es��h\^kr�^;eCSOm ��S@r�Vbe�V8c-^wWEZXYO[�r�^�rqVba � �� ® &²�VXr���[=r�e>6Å�/ � "C®�K � ®�M/²�²�6 � �   �@sÃ��h=^

WESU_�_`^Qr��+S-a=f/V8a\T�YOe�SUgqr�f/^;�=a\^ Y���^;_`�\_�YOa=fCgqS/f/^QZ��l]�h\^Q_�^�Y�TU_�SU[\a=ftYOe�S-g VXr�e`_�[=^V8a��ÅVbÇ � �� 6Cs(��SOe`^ e�h=YOe�"C®�K � ®:>;²�²"VXr�m�YOZXr�^ V8a �5moSU_�YOZ8Z � �à\s�a/moSU_�e`[\a=YIe`^;Z8� � �� ® &²MV8r�V8a/�=a=V}e`^�YOa=f�e�hd[=r�e�h\VXr�gqS/f/^;Z\VXr�a\S-e(�\_`Sdf\[=WE^�f�V8a��=a\Vbe�^;Z8�

gCYOad�År�e`^;�=rQs� �m�]�^tY-�\�\Z8� � � e�S!&»e�h=^;a¹Vbe�VXr�^QYUr�V8Z8�5c-^Q_�Vb�=^�f5e`h=YIe � � � ® &² �'&�¿e�h=V8r�T-V8c-^�r�[=r�e`h\^�YOa�r�]"^;_�e`h=YIe &nVXr�r`YIe�VXr���YO�\Z8^-�U�\[/e"]�^�f/S�a\SOe�h�Y�c-^�YOad��V8a/moSU_�gCYIe`VbSUaYO�+S-[\e�g�S/f/^QZ8rQs

>��KA�������H��RLF�P�H+D �\DMJÃF ���� �dN-P ��P�H+D�� GIH ��� ��*°A�3AR?�A������ �@NUP ��P�H+D�� GIH ������*°A ��h\^�f/^QW;V8r�VbSUa �\_�SU�\Z8^;g ®�S-_3e`h\^�¯`�(a@e`r`W�h\^QV8f/[=a\TUr�j

�\_`S-�\Z8^;gC±@²�SOm�=_`r�e�j�S-_�f/^Q_�Z8S-T-VXW�WQYOat�+^�e�_�Y-WE^�fC�=YUW�i�V8a@e�S�e�h\^�^QY-_�Z8���-^QY-_`r�SOmKe`h\^{�O Ie`hWE^Qa@e�[\_`�-sM��_`S-[\a=ft|Q¶U�- ���V8Z8��^Q_�eMmoS-_`g�[\ZXYIe`^Qf�e`h\^��=_�SU�\Zb^Qg#e�S���a=f�Y-a�YOZ8T-SU_�Vbe�h\g#]�h\VXW�hf/^�WEVXf/^Qr�e�h=^�cIYOZ8V8f\V}e���SOm�moS-_`g�[\ZXY-r�Vbaw��_`r�e�j�S-_�f/^;_��\_�^�f/VXW;YIe`^�Z8S-TUV8Wt®Rr�^Q^�^Us T�s�v � �-y«²Es���^W;Y-ZbZ8^Qfne`h\V8r�f/^QW;V8r�VbSUan�=_�SU�\Zb^Qg e�h=^�È�§/¡+Ê-�O�q�;¡=���I�/¨+¤�¥UªE�b�;� ¥�È �C�I�o�\�;�q�O�R�����O���b¥`Ë-���Esu�^;e�]�^Q^;a#|Q¶@�O 5Y-a=f¸|�¶-¾U 5Yz��S@r�Vbe�V8c-^�r�S-Z8[/e�V8S-a»SOm�e�h\^wf/^�WEVXr�V8S-aº�\_�SU�\Z8^;g r�^;^Qg�^�f

e�Sw�+^Cgq^;_`^;Z8�5Y�Ð@[\^Qr�e�V8S-azSOm"gqYOe�h\^QgCYIe�VXW;Y-Z�VbadcU^;a@e�V8S-aKsq �a=f\^;^QfÅr�S-gq^q�\_`S-T-_`^Qr`r�]"YUrY-W�h=Vb^Qc-^Qf�r�SdSUa�YUrMf\^QWEVXf\Y-�\Zb^�r�[\�1WEZXY-r`r�^�r�S-m��\_`^Qf\V8WQYIe�^"Z8S-T-VXW"]�^Q_�^�moS-[=a=f3s���h\^�f/^QW;V8r�VbSUaYOZ8T-SU_�Vbe�h=gqr��\_`SIcdV8f/^�fCmoSU_�e`h\^Qr�^{WEZXY-r`r�^�r�]"^;_`^�W;Zb^�YO_`Zb�q^EÇ1^QWEe�V8c-^ V8anYOad�CV8a@e�[\Vbe�V8c-^ r�^Qa=r�^SOm3e`h\^�]�SU_`fw®�a\SOe`^�e�h�YIe��+^EmoSU_�^��\[\�\Z8VXW;YIe`VbSUatSOm��[\_`Vba=T= r(ZXYOa=f/gCY-_�i��=YO�+^;_��da\S{moSU_�gCYOZWESUa=WE^Q�/e�SOm�Y-ZbTUS-_`V}e`h\g ]�Y-r�Y�cIYOV8Z8Y-�\Z8^�²�s ��a\^lSOm�e`h\^5��_`r�en_`^Qr�[\Zbe`rz®�Y-W�h=Vb^Qc-^Qf¸^;c-^Qa�+^EmoS-_`^qe�h=^CT-^;a=^;_�YOZ��\_`S-�\Z8^;g ]"YUr�moS-_`g�[\ZXYIe`^Qfl�@�l��V8Zb�+^;_�e�² ]�Y-r�e`h\^tf/^�WEVXf\YO�\V8Z8V}e��lSOme�h=^�g�SUa=Y-f\V8W�WEZXY-r`r�v ¾@��yK®oV�s ^-sMe�h\^�W;Z8YUr�r�S-m=�=_�r�e�SU_`f/^Q_MmoS-_`g�[\ZXY-r�WESUa@e`YOV8a\V8a\T�S-a\Z8�{[\a=Y-_���\_`^Qf/VXW;YOe�^E¼ºYOa=fÃa\Sµmo[\a=W�e`VbSUa¸r��dg���SUZ8r�²�s& �aÃe�h=^lr`YOgq^w�=YO�+^;_���½SU]�^Qa\h\^;V8g �=_�SIcU^Qfe�h�YIe�f\�UY-f\V8WqZ8S-TUV8Wk®�VRs ^-s�e`h\^nr�[\�1WEZXY-r`r{]�h\^Q_�^�Y-ZbZ��\_`^Qf/VXW;YOe�^tr��@g���SUZ8r�YO_`^C�\V8a=YO_`�\² V8rY¸¤`�`ÊO§=�E����¥I¡&�E�8��¦�¦���V�s ^Us Y´WEZXY-r`rCS-m{�=_`r�e�j�S-_�f/^Q_qmoS-_`g�[\ZXY-rC^;Ç+^�W�e`VbcU^;Z8�»^Qa=WES/f/V8a\T¹mo[=ZbZ�\_`^Qf/VXW;YOe�^CZ8S-TUV8W-sn �aze�h=^Ce�V8gq^t��^;e�]�^Q^;a¹]"S-_`Z8fz]�YO_{ {YOa�fl]"S-_`ZXfl]�YO_{ � �\_�SUgqVba\^Qa@eZ8S-T-VXWEVXYOa�r�YOe�e`YUW�i-^�f�e�h\VXr��\_�SU�\Z8^;g�s���h=^�V8a\Vbe�VXYOZ�r�e`_`YOe�^QT-�Å®o�\_`S-�=Y-�\Z8�/²�]"YUr�e`S�^Qa\Z8Y-_�TU^e�h=^�f/^QW;V8f=YO�\Z8^CWEZXY-r`r�^�r{YOa=fle�Sï`r�h\_`V8a\i/±�e`h\^C_`^Qf/[=WEe�V8S-a¹WEZXY-r`r�^Qr�e�V8ZbZ�e�h\^Q�5^Qc-^;a@e`[=YOZ8Zb�gq^;^;e�YOe�r�S-gq^��+S-V8a@e ®oe�h\^�S-[\e`WESUgq^�]"S-[\ZXfCh=Y�cU^��+^;^;a�e�h\^{f/^�WEVXf\YO�=VbZ8V}e��qS-mK�=_�r�e�j�SU_`f/^Q_Z8S-T-VXWQ²Es¹u�[\e�V8aÍ|�¶-¾-Ì5��s�!�hd[\_`W�hºr�[=WQWE^Q^Qf/^�f¹e�Sl�\_`SIc-^te`h\^�[\a=f/^�WEVXf\YO�\V8Z8V}e��¹S-m��=_`r�e�jS-_�f/^Q_"Z8S-TUV8W�YOa�fte`h@[�r"e�h\^q§/¡\¦;¥O�¬©��UªE�«�}�«�R¢ SOm�e�h\^C®�T-^;a=^;_�YOZ«²�f/^�WEVXr�V8S-a��\_`S-�\Z8^;g vb|Q Oy�s���aV8g�gq^�f/V8YOe�^�W;S-a=r�^QÐ@[\^Qa=WE^�SOmK!�hd[\_`W�h r�_`^Qr�[\Zbe�]�Y-r�e`h\^�[\a=f/^�WEVXf\YO�=VbZ8V}e���SOm3YOZ8Z/_�^�f/[=W�e`VbSUaWEZXY-r`r�^QrQs ��^�r��=V}e`^�e`h\V8r�a\^QTUYIe`VbcU^(_`^Qr�[\Z}e���e�h\^"Vba@e`^;_`^Qr�eVba�e�h\^�f/^QW;V8r�V8S-a{�\_`S-�\Z8^;g&]�Y-ri-^;�\eYOZ8V8c-^-�Ke�h\^�moS/WE[=r{r�h\Vbm«e�V8a\T�e�S�e�h=^�^;À/�\ZbSU_`YOe�V8S-alSOm�e`h\^q��SU_`f\^;_`ZbV8a\^���^;e�]�^Q^;aÅf/^QW;V8f\Y-�\Z8^YOa�fn[=a=f/^QW;V8f=YO�\Z8^{WEZXY-r`r�^�r;s

Page 23: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � �-¾

�aÍgqS-_`^k_`^QWE^Qa@en_`^Qr�^QYO_�W�hÃS-a°e`h\^lf\^QWEVXr�VbSUa¸�\_`S-�\Z8^;g e�h\^År`YIe�VXr���YO�\V8Z8V}e��»�\_`S-�\Z8^;gV8a=r�e`^QYUfnS-me`h\^{cIYOZ8V8f/Vbe����=_�SU�\Zb^Qg VXr�Vbadc-^�r�e`VbT@YIe`^Qf3s�u�Y-r�V8WQYOZ8Zb�qe`h\VXr�V8rM��[�r�e�Y�gCYIe�e�^;_�SOme`YUr�e`^�Y-r &VXr�cIYOZ8V8f�VbÇ "� &V8r�[\a=r`YIe�VXr���YO�\Z8^-s���+SIc-^�]"^tgq^;a@e`VbSUa\^QfÅe`h\^�g�SUa=Y-f\V8WtY-a=fÅe`h\^nf/�@Y-f/VXWtW;Z8YUr�r�^Qr�]�h\V8W�hºYO_`^�W�h=YO_�Y-WEj

e�^Q_�V8p;^�f´�d�Åe`h\^�Y-_�Vbe��¹SOm��\_�^�f/VXW;YIe`^�r��dg��+S-ZXr;sµ��a\SOe`h\^;_�e��d�+^�S-m�r��@a@e�YIÀµ_`^Qr�e�_`V8WEe�V8S-aWESUa=WE^Q_�a�r�e`h\^nÐ@[=Y-aUe`V}��^;_��\_�^;�\À¹SOm��=_�^Qa\^EÀzmoS-_`g�[\ZXY-rQs¹�dS-gq^�S-m�e�h\^��\_`^;a\^;ÀµWEZXY-r`r�^�rr�h\SI]�alf/^�WEVXf\YO�=Zb^w®oV�s ^-s�e`h\^Cr�YOe�VXr��+YO�\V8ZbVbe��w�\_`S-�\Z8^;g S-m�e`h\^Qr�^CWEZXY-r`r�^�r�]�Y-r��\_`SIc-^�fkf/^EjWEVXf\Y-�\Zb^�²���^;moS-_`^��\[=�\ZbVXW;YOe�V8S-a�SOm3!�hd[\_�W�hK r_`^Qr�[\Zbe�Y-_�^U�F� � � ®oe�h\^����3(U�;¤��q�O¡=¡��;�b��¦�¦"vb|Eyo²������ � ®«e`h\^����¥-ÊU�E���E�b�I¦�¦ v �/|;y«²E�\YOa=fI� � � � ®«e`h\^����E¤�¡1�I¢�¦� �3�`��¥I¡�Æ(¡ (U�;�M�;�b��¦�¦{v ��y«²Es�dZbV8T-h@e�W�h=YOa\TU^Qr�Vba°e`h\^5�=_�^;�\À/^Qr�Y-��SIcU^kZ8^QY-f»e`S´[\a�f/^QW;V8f\Y-�\Z8^lWEZXY-r`r�^QrQ��^-s T=s ��� �

YOa�f ���� ��f\^E�=a\^q�\_`^;a=^EÀlW;Z8YUr�r�^Qr�]�V}e`hl[=a=f/^QW;V8f=YO�\Z8^Cr�YOe�VXr���Y-�\V8ZbVbe��w�\_`S-�\Z8^;gCrQs�%\SU_{Ye�h=S-_`S-[\TUh�e`_�^�YIe�gq^QaUe�S-m�e`h\^�f/^QW;V8r�V8S-a��\_�SU�\Z8^;g$YUr�Y�]�h=S-Z8^ r�^;^Cv ¶Iy�s��h\^qg�^;e�h\S/f\r Y-�\�\Z8Vb^�fke`Sn�\_`SIc-^�f/^QW;V8f\Y-�\V8ZbVbe��wSOm�WEZXY-r`r�^�r�Y-_�^�YIe Zb^�Y-r�e YUr�V8a@e�^;_`^Qr�e�j

V8a\T¹Y-r�e�h\^kW;Z8YUr�r�^Qr�e�h=^;gCr�^QZbcU^QrQsº �a»�=Y-_�e`V8W;[\Z8Y-_Q�(e�h\^wf/^�WEVXf\YO�\V8Z8V}e��µS-m�e`h\^wu�^Q_�a�Y��dr�¼�/W�h½SUa/�=a\iU^;Z�WEZXY-r`r�WQYOak�+^��=_�SIcU^Qf�cdV8Yte�h\^��=a\Vbe�^E¼@gqS/f/^;Z}¼@�\_`S-�+^;_�e���S-m�e�h\VXr WEZXY-r`r�®�VRs ^-se�h=^;_`^�^EÀ/VXr�e�r�Yq��a\V}e`^�gqS/f/^;ZMVbÇle`h\^;_`^�^EÀ/VXr�e�r�YCgqS/f/^QZMYOe�YOZ8Z«²�s�� W;Z8YUr�r�^;aI��SI�dV8a\Tqe�h=V8r�\_`S-�+^;_�e���VXr"W;YOZ8Z8^Qf�Æ�¡=�«���E�¬¢q��¥I¡=��¤�¥O�«�b�-ª;�b�;s��wSUr�e�S-m3e�h\^�S-_`VbTUVba=Y-Z=�\_`SdSOm�r�SOmf/^�WEVXf\YO�\V8Z8V}e��moS-_�e`h\^�WEZXY-r`r�^Qr�g�^Qa@e�V8S-a\^�f�Y-��SIcU^�]"^;_`^��=Y-r�^Qf�S-a�e�h\^��=a=V}e`^�¼@gqS/f/^QZ¬¼d�\_�SU��^Q_�e��UsK �a�m�Y-WEee�h=^ r�^Ee�S-m�YOZ8Z1�=_�r�e�j�SU_`f/^Q_(moSU_�g�[\Z8YUr�h�Y�c@V8a\T��=a\Vbe�^ gqS/f/^;ZXr"V8r�_`^QW;[\_`r�V8c-^;Z8��^;ad[\gq^;_�YO�\Z8^-s��hd[=r�V8an�+^;_�moS-_`gqVba=Tqr�^QY-_`W�h�moS-_�Y�_�^;mo[/e`YOe�V8S-awYOa�ftmoSU_�Y���a\V}e`^{gqSdf\^;Z3V8a���YO_�YOZ8Zb^QZR�d]"^S-�\e`YOV8aÃYlf/^�WEVXr�V8S-aº�\_`SdW;^Qf/[=_�^Us»!�Zb^�YO_`Zb�ze`h\^Qr�^�g�S/f/^QZ}j�e�h=^;S-_`^Ee`V8W�gq^Ee�h=Sdf=rq]�^Q_�^�f/^Ejr�VbTUa\^Qfne�SC¨+¤�¥O©���f/^QW;V8f\Y-�\V8ZbVbe���_�YIe`h\^;_�e`h=YOa�e`StT-V8c-^ ^EÁtW;Vb^QaUe�f/^QW;V8r�VbSUawYOZ8T-S-_`Vbe�h\gCrQs� �am�Y-WEeQ�=e�h\^�Y-ZbTUS-_`V}e`h\gCr�^;Àde�_�Y-W�e`^Qf�mo_�SUg e`h\V8r�g�^;e�h\S/f�YO_`^ �=Y-r�^Qf�SUan^;Àdh�YO[=r�e�V8c-^{r�^QYO_�W�hYOa�fÅh=YO_�f/Z8�5YO_`^tW;Y-a=f/VXf\YIe`^Qr moSU_�YOa¹^;cU^;azgqSdf\^Qr�e����I�b�;§/�¬§d¦C¤��I����¥��E�«¡1�I��¥I¤�s� �e�e�[=_�a\^�fS-[\e�e`h=YIe�e�h\^qr�YOe�VXr��+YO�\V8ZbVbe����\_�SU�\Z8^;g SOm�f/^�WEVXf\YO�=Zb^�WEZXY-r`r�^�r�W;Y-ak�+^�h=Y-a=f/Z8^Qfw�d�n¨+¤`¥Q¥�È�o�\��¥I¤��;������gq^QY-a=r�SUaµYwZXYO_`T-^;_�r`W;Y-Zb^Usk��h\^tgqSUr�e�Y-�\�\_`S-�\_`V8YOe�^CW;Y-a=f/VXf\YIe`^CmoS-_�r�[�W�hµY�\_`SdSOme`h\^;SU_�^;e�VXW{YO�\�=_�S@Y-W�htVXr{¤��E¦;¥I�¬§/����¥I¡�s�3A �3A�������H��RLF�P�H+D � �dN-P��QPRH�D �MG�HN �dJ�L�G.���-A �d[\�\�+SUr�^�e�h=YOe�]�^Cr�e`Y-_�e�Yne�h\^QS-_`^;g

�\_`SIc-^Q_�®oV�s ^UslYlWES-gq�\Z8^Ee`^t_`^Qr�S-Z8[/e�V8S-a¹_`^E�=a=^;gq^;a@e � % ²�S-aµYlr�^;e�SOm�W;Z8Y-[=r�^�r &°]�h\VXW�hgCY��t�+^�r�YOe�VXr���Y-�\Z8^�SU_�[\a=r`YIe`V8r���YO�=Zb^Us(���dcdV8S-[=r�Zb�qe`h\^;_`^�YO_`^�e�h\_`^;^{�+SUr`r�V8�\V8ZbVbe�V8^QrQ�|-s � % e`^;_`gqVba=YOe�^�r�S-a &lYOa�f�_`^Emo[/e`^Qr &�su"^QWQYO[=r�^ � % VXr�WES-_`_`^QW�e�YOa�f � � � % ® &K²�]"^{ida\SI]¸e`h=YIe &lVXr�[\a=r`YIe`V8r���Y-�\Zb^Us

�/s � % e`^;_`gqVba=YOe�^�r�S-a &5]�Vbe�h\SU[/e�f/^;_`V8c@V8a\T � su"�Ce�h=^�WES-gq�\Z8^Ee`^;a\^�r�r�S-m � % &5g�[�r�e��+^�r�YOe�VXr��+YO�\Z8^-s

¾\s � % f\S@^�r�a\SOe�e`^;_`gqVba=YOe�^ S-a &�� �ate`h\VXr"WQY-r�^ � �% ® &K²�®oe�h\^ r�^;e�SOm�Y-ZbZ1WEZXYO[=r�^Qr�f/^Q_�V8cIYO�\Z8^��d�� % mo_`S-g &²�V8r"V8a/�=a\Vbe�^YOa�f � �� � �% ® &²�®o]"^�YUr�r�[\gq^�e�h�YIe�e`h\^��=_�S/f/[=WEe�V8S-atS-m3a\^;]¸W;Z8Y-[=r�^�r(VXr�r�e�SU�\��^�ftY-rr�S@SUanYUr � VXr�f/^Q_�V8c-^�f=²�s��KV8i-^ V8awW;Y-r�^��-² &lVXr�r`YIe�VXr���YO�\Z8^-�/�=[/e�]�^{WQYOa\a\S-e�f/^Ee`^QW�ee�h=V8r��\_`S-�+^;_�e��{��[=r�e��d��WESUgq�\[/e�V8a\T� �% ® &K²Es

��r�W;Z8Y-[=r�^"Z8S-TUV8W�¼��+^;V8a\T�Y�_`^Qf/[=WEe�V8S-aCWEZXY-r`r�SOm1�=_�r�e�j�S-_�f/^;_�Z8S-T-VXW�¼�V8r([\a=f/^�WEVXf\YO�\Z8^�]"^ida\SI]°e`h=YIe�moS-_�^Qc-^;_`�CWESUg��=Zb^;e�^ _�^;�=a\^Qg�^Qa@e"SU��^Q_`YOe�S-_ � % e`h\^;_`^�g�[=r�e�^;À/V8r�e�Y�®o�=a\Vbe�^�²r�^Ee�S-m(WEZXYO[=r�^Qr &År;s eQs � �% ® &²�V8r��«¡QÆ�¡=�«���Es���h=YOe�gq^QYOa�r�Vbe�VXr;��Vbaw�\_`V8a=WEV8�\Z8^-�+Vbgq�+SUr`r�V8�\Z8^e�SkY�cUS-VXfwa\SUaUe`^;_`gqVba=YOe�V8S-azS-aÅYOZ8Z(r�^;e`r S-m"WEZXYO[�r�^�r;sq�K^;e�[=r VbadcU^Qr�e�V8TUYIe`^�e`h\VXr{��SUVba@e{V8ar�S-gq^;]�h=YOe�g�SU_�^{f/^;e`Y-VbZ���K^Ee�ÎÄ��^zYµr�^Qa@e�^;a�WE^kS-m�®«�=_�r�e�j�SU_`f\^;_�²��\_�^�f/VXW;YIe`^kZ8S-T-VXWOs·�r�V8a\TºYµa\S-_`gCYOZ�moSU_�g

e�_�YOa�r�moSU_�gCYIe`VbSUal]"^tW;Y-aze�_�YOa=r�moS-_`g Î�Vba@e`SkYwr�YOe�¼@^�Ð@[\VbcIY-Zb^QaUe�r�^Ee�S-m�W;Z8Y-[=r�^Qr &�snu"�

Page 24: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

� � )1*O,/.1)+0123,/4k*-,/687+9;:=<e�h=^�YO_`T-[\gq^;a@e�r"Y-��SIcU^ � % g�[=r�e���^ a\SUa@e�^;_`gqVba�YIe�V8a\T�S-a�r�SUgq^���a\V}e`^-�=r`YIe`V8r���Y-�\Zb^ r�^Ee`rSOm�WEZXYO[=r�^QrQ¿@e�h\^Q_�^;moS-_`^�WQY-r�^�¾@²(gq^QaUe`VbSUa\^Qf�YO�+SIc-^�W;Y-a\a\SOe��+^ Y�cUS-VXf/^QftVba�T-^Qa\^;_�YOZ�sMu"[/eY�c-SUV8f\Vba\TwWQY-r�^t¾U²�moS-_�r��+^QW;V}��Ww¦�§=ª��;�b��¦�¦;�E¦�S-m�W;Z8Y-[=r�^CZ8S-TUV8WqVXr{�\_`^QW;V8r�^;Z8�ke`h\^t�\_`V8a=WEV8�\Z8^SOm ¤��E¦;¥I�¬§/����¥I¡ÃÊ-���E�X¦���¥O¡k¨1¤�¥Q����ÊI§/¤`��¦��� �e�Zb^�Y-f\r�e`S�e�h\^qmoSUZbZ8SI]�V8a\T�g�^;e�h\S/flmoS-_{�=_�SIcdV8a\Tf/^�WEVXf\YO�\V8Z8V}e��nSOm"®oe�h\^�r�YOe�VXr���Y-�\V8ZbVbe��C�\_`S-�\Z8^;g�SOm`²�Y��=_�r�e�j�SU_`f\^;_�WEZXY-r`r �(���� �_�YOa�r�moSU_�gÍe�h\^�moSU_�g�[\ZXY-r1V8a �qVba@e�S�e�h\^QVb_r`YIe�j�^�Ð@[\VbcIY-Zb^QaUeW;Z8Y-[=r�^�moS-_`gqr�®o_`^Qr�[\Z}e`Vba=TV8a�YCW;Z8Y-[=r�Y-Z3WEZXY-r`r �ÏKW;S-_`_�^�r��+S-a=f\Vba\T�e�S��M²�s

� � %MV8a=f�Y�W;S-gq�\Z8^Ee`^{_�^�r�SUZb[/e`VbSUa�_`^E�=a=^;gq^;a@e�]�h\VXW�h�e`^;_`gqVba=YOe�^�r�S-a��ÏRs��h\VXr��\_`V8a=WEV8�\Z8^CV8r�Ð@[\Vbe�^CTU^;a\^Q_`Y-Z(YOa=fÅWQYOaÅ��^nYO�\�\Z8V8^Qfz]�V}e`h¹SOe`h\^;_�WQYOZXWE[\Z8V�e�h�YOa¹_`^Qr�jS-Z8[/e`VbSUalYOa�fkSOe`h\^;_�a\SU_�gCYOZ�moS-_`gCr�e`h=YOazWEZXYO[=r�^�moSU_�g�s �a´|�¶-ÌUx��1s ��sK�kYUr�Z8SIcn�=_�SIcU^Qfe�h=^�f/^�WEVXf\YO�\V8Z8V}e���SOm3e`h\^�r�S�W;Y-ZbZ8^Qf���¼/WEZXY-r`r�®�Y�f\^QWEVXr�VbSUatWEZXY-r`r(�\_`S-�+^;_`Zb��WESUaUe�YOV8a\V8a\T e�h\^�q½SUf\^;Z\WEZXY-r`r�²3[=r�Vba=T Y�r�VbgqV8Z8Y-_MY-�\�\_`SUY-W�h¿IV}e�VXr���Y-r�^Qf�SUa�e`h\^�r�S W;Y-ZbZ8^Qf�Vbadc-^Q_`r�^�gq^;e�h\S/f3�]�h\VXW�hqV8r(Y�_`^Qr�S-Z8[/e�V8S-a/¼Ue��d��^"gq^Ee`h\S/f�moS-_`g�[\ZXYIe`^Qf�]�V}e`h\Vba�e`h\^�mo_`Y-gq^;]"S-_`i{SOm3Y�r�^QÐ@[\^Qa@eW;Y-Z8W;[\Z8[=r�v ¾ �Oy�s �a�e`h\^"r`YOgq^�r��=Vb_`V}e�Y-rM�kYUr�Z8SIc1���=[/eMSUa�e`h\^��=Y-r�V8r�SOm=e�h\^"_�^�r�SUZb[\e�V8S-a�WQYOZXWE[\Z8[=rQ���-SI�da\^Q_

r�h\SI]�^�fqVbanh\VXr(e`h\^Qr�V8r�v �OÌIy+e�h�YIe�_`^Qr�S-Z8[/e`VbSUaqe�h\^QS-_`^;g­�\_`SIc-^;_�r(WQYOat�+^�[=r�^QfnY-r�f/^QW;V8r�VbSUa�\_`S/WE^Qf\[\_�^�rMmoS-_(r�S-gq^�WEZXY-r`r�VXW;Y-Zd�\_�^Qa\^EÀ�WEZXY-r`r�^�r"®�^-s T=s�e�h\^���W�i-^Q_�gCYOa=ad¼{Y-a=f�e�h\^��q½S@f/^;ZWEZXY-r`r�²�s���V8r�VXf/^QYqe`St�=a�fkWESUg��=Zb^;e�^�_`^Qr�S-Z8[/e`VbSUaw_�^;�=a\^;gq^QaUe�r � % ]�h\VXW�hwe`^;_`g�V8a=YOe�^�SUaWEZXYO[�r�^�W;Z8YUr�r�^Qr�WES-_`_`^Qr���SUa=f/V8a\T�e�St�\_`^;a=^EÀ�W;Z8YUr�r�^QrQ�=Z8^QYUfne�SCe`h\^�TU^;a\^Q_`Y-ZKgq^Ee�h=Sdf\S-Z8S-T-�SOm�_`^Qr�S-Z8[/e�V8S-a�f/^QW;V8r�VbSUa��\_�S/W;^Qf/[\_`^Qr�f/^Qc-^QZbSU��^�f�V8a¹v}| �Oy�s�(c-^Qan[=a\_�^�r�e`_�VXW�e`^Qf�_�^�r�SUZb[/e`VbSUa�WQYOan��^{[=r�^Emo[=ZKVba��\_`SIcdVba\T�e�h=^ f\^QWEVXf\Y-�\VbZ8Vbe��tSOm��=_`r�e�j

S-_�f/^Q_"W;Z8YUr�r�^QrQsM��a�^;À/Y-gq�\Zb^�V8r���^;_`�\_`Y-a=f3 r�W;Z8YUr�r � !&v �O¾Iy��@]�h\^;_`^ � !ºVXr�e�h\^ WEZXY-r`r�SOmYOZ8Z3�=_�r�e�j�S-_�f/^;_�moS-_`g�[\ZXY-r�S-me`h\^ moS-_`g

®�. 4?�F4Q² &(&�&Q®�. � � � ²E®�� 45',&�&(& '�� � ²moS-_�mo[=a=W�e`VbSUa/jRmo_`^;^{Z8Vbe�^;_�YOZXr�� 4 %�2 2�2 %�� � s� ������� ���­~/s8|���1�=��¦;�O�R�X¦oÆ��UªE�«�}�«�R¢�¨+¤�¥UªE�b�;� ¥�È��°�X¦�Ê-���;��Ê-�-ª;�b��� ��������F���diUS-Z8^;gqV8pQYIe`VbSUawSOm(moSU_�g�[\ZXY-r�V8a � !#f/V8_`^QW�e`Zb���dV8^;ZXf\r�YnWEZXYO[=r`YOZ�WEZXY-r`r � !�Â

WESUa=r�V8r�e�V8a\TqSOmM�=a\Vbe�^�r�^Ee�r�SOm�[\a\Vbe�WEZXYO[=r�^QrQs���SI]ÍZ8^Ee&5� � 4 %�2 2�2 % � �� %OB 4 � %�2�2 2 %JB � � �

moS-_�r�SUgq^�YIe`S-gCr 4 %�2 2�2 % � %JB 4 %�2 2�2�%OB��1¿�e`h\^;a�(WEZ8^QYO_`Z8�-� � � ® &² � &ÃS-_ � � ® &² �&�� � �@s���hd[=r{moSU_�YOZ8Z & � � !� � � ® &² VXr �=a\Vbe�^nYOa=f3��WESUa=r�^QÐ@[\^;a@e`Zb�U�[\a\_`^Qr�e�_`VXW�e�^�f_`^Qr�S-Z8[/e�V8S-a�f/^QW;V8f\^Qr � !�Â=Y-a=fte`hd[=r � !�s %��h\^��=_�SdSOm(S-m(e�h=^�e`h\^;SU_�^Qg Y-��SIcU^�r�h\SI]�r�e`h\^���SI]"^;_�SOm(e`h\^�[=a\V}�+W;YIe`VbSUa5�\_`V8a=WEV8�\Z8^

]�h\VXW�h�_�^Qa=f/^;_�r�YOa�S-_`V8T-V8a=YOZ8Zb�tW;S-gq�\Z8V8WQYIe`^Qfn�\_�SU�\Z8^;g e`_�V8cdV8Y-ZRs��SI]"^;c-^Q_K[\a\_`^Qr�e�_`VXW�e�^�f _�^�r�SUZb[\e�V8S-a�m�YOV8Z8rS-a{cU^;_`��r�Vbgq�\Z8^�®Rr�YOe�VXr���Y-�\Z8^�²3r�^Ee�rKSOm=W;Z8Y-[=r�^QrQ��������������5~/s8|����K^;e�Î �="C®0M/² 'q®E���1²E®�"C®$�+²$� ";"C®HK�®$�+²�²�²Es(��h\^;atÎ V8r�r�YOe�VXr��+YO�\Z8^

YOa�fz®�cdV8Y�e�h=^�r�e�YOa=f\Y-_`f�e�_�YOa�r�moSU_�gCYIe`VbSUa�²��@V8^;ZXf\r"e`h\^�r�^;e�SOm�WEZXYO[=r�^Qr& � � "C®0M/²E¿ � "C®0�+²3%J"C®�K�®0�+²�²�¿�"C®0�+²?%O"C®�K�®0�+²�² � � 2

��r�&°VXr�r`YIe`V8r���YO�=Zb^ � �� � � ® &²�sÅ�wS-_`^;SIcU^;_�� � "C®0�+²3%J"C®�K N ��� 4 ®$�1²�²�� � � ® &² moSU_�Y-ZbZ� �� ���/e`h@[�r � � ® &²"VXr�V8a/�=a\Vbe�^�Y-a=f�_`^Qr�S-Z8[/e`VbSUa�f/Sd^�r�a\SOe�e`^;_`g�V8a=YOe�^ S-a &�s���\�\Z8�dVba=T�e�h=^���j�S-_�f/^;_`V8a\T�_�^;�=a\^Qg�^Qa@e �� � ®Rr�^Q^���À\Y-g��=Zb^ ��sb|�²�e�S�e�h\^�r�^Ee�SOm=WEZXYO[�r�^�r

&µV8al��À\Y-g��=Zb^q~/s8|�]"^���[=r�e{S-�/e�YOV8a � � � ® &² � &�� "C®0�+² � "C®0�+² �@s��dS � �� � � � ® &K²YOa�f3�\�d�Ce�h=^�WES-gq�\Z8^Ee`^;a\^�r�r�S-m � � �/]"^�WESUa=WEZ8[=f/^�e�h�YIe &5VXr�r`YIe�VXr���YO�\Z8^-s �

Page 25: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � �U~

�� � f/Sd^Qr�a=SOe(S-a=Zb��]"S-_`i{V8aq�(À\YOgq�\Z8^�~\sb|"�\[/e�T-V8c-^Qr�Y f/^�WEVXr�V8S-a��\_`SdW;^Qf/[=_�^�SOm1r�SUgq^]"^;Z8Z}j�ida\SI]�a���_`r�e�j�S-_�f/^;_�WEZXY-r`r�^QrQ�/Vba��=YO_�e�VXWE[=Z8Y-_�SOme`h\^���W�iU^;_`gCYOa\a�WEZXY-r`r;��K^Ee�[�r�WESUa=r�VXf/^Q_�Y�moSU_�g�[\Z8Y�S-m�e`h\^ moS-_`g

Îz�Å®��)� 4Q² &(&(&Q®��)� � ²;®E�F /²;®��!1 4;² &(&�&Q®���1 --²��­®$� 4 % 2�2 2 %#� � %O1 4 %�2�2 2�%J1 -�%J /²]�h\^Q_�^ ,F% � �° CYOa�f�� VXr�Y�mo[\a=WEe�V8S-ad¼nY-a=f�WES-a�r�e�YOa@e�mo_�^Q^{gCYIe�_`VbÀ1s�u���r�iUS-Z8^;gqV8p;V8a\TÎ ]�^ S-�\e`YOV8awY�moS-_`g�[\ZXY

Î Ï �z®��� \²��­® � 4 %�2 2�2�% � � %OK�4O®$ \²?% 2�2�2 %LK -/®0 /²3%# \²?%]�h\^Q_�^ � 4 % 2�2�2 % � � YO_`^t®�f/VbÇ+^Q_�^Qa@e�²�WES-a�r�e�YOa@e�r��@g���SUZ8r�YOa=f K 4 %�2 2�2 %LK -qYO_`^�®�f\V}Ç1^;_`^;a@e�²S-a=^�¼@�=Z8YUWE^�mo[=a=W�e`VbSUalr��@g���SUZ8rQs� �ake�_�YOa�r�moSU_�gqV8a\TCe�h=^�gCYIe`_�VbÀwSOm�Î{Ï�V8aUe`S�W;S-aI��[=a=W�e`VbcU^a\SU_�gCYOZ�moS-_`g ®ocdVXY¹e�h=^zr�e`Y-a=f\YO_�fÃe`_`Y-a=r�moSU_�gCYOe�V8S-a�²q]"^5SU�/e`Y-Vba Y´r�^Ee�SOm�WEZXYO[�r�^�r &mo[\Zb�=Z8ZbV8a\TCe`h\^ moS-Z8ZbSI]�V8a\T��\_`S-�+^;_�e�V8^QrQ�|�²���Z8ZW;Z8Y-[=r�^�r�WES-a@e�YOV8a�YOe�g�S@r�e�SUa\^ c�Y-_�VXYO�=Zb^U��-²�YOZ8Z1mo[\a=WEe�V8S-awr��@g���SUZ8r�S/WQWE[\_`_�V8a\T�Vba &lY-_�^ [\a�YO_`�-�¾U²�e�h=^ e�^;_`g$f/^Q�/e�h�S-m�Y-ZbZKW;Z8Y-[=r�^�r � V8a &5VXr � |Us �ak�=YO_�e�VXWE[=Z8Y-_�YOZ8Z�r�^Ee`r�SOm(WEZXYO[�r�^�r�S-�/e�YOV8a\^Qfnmo_`S-g�e�h\^���W�i-^Q_�gCY-a\awWEZXY-r`r���^QZbSUa\TCe`S

e�h=^{g�SU_�^ TU^;a\^Q_`Y-Z�¥O¡+� �-©I�I¤����UªE�b���E�b�I¦�¦�V8aUe`_�S/f/[�WE^Qf�V8a�e�h\^ moSUZbZ8SI]�Vba=T�f/^;�=a\Vbe�V8S-aK�� �����������������»~/s8|�����h=^nWEZXY-r`r������� t®�YOZXr�S5W;Y-ZbZ8^Qfze`h\^�SUa\^�¼dc�Y-_�VXYO�=Zb^CWEZXY-r`r�² V8r�e�h\^

r�^EeCSOm YOZ8Z��=a\Vbe�^wr�^;e`rqS-m�WEZXYO[=r�^Qr�&¸mo[=Z}�=Z8Z8Vba\Tze`h\^�moS-Z8ZbSI]�V8a\TÅWES-a�f/V}e`VbSUaK����Z8Z � � &WESUa@e`YOV8a�YIe�gqSUr�e�S-a\^ cIYO_`V8Y-�\Z8^-s'l^th�Y�c-^tr�^;^;aze`h=YIe�e`h\^�W;Z8Y-[=r�^�moSU_�gCr{S-m"e`h\^CmoSU_�g�[\Z8YUr SOm"e�h\^n��W�i-^Q_�gCY-a\a¹WEZXY-r`r

�+^;Z8S-a\T�e`S������� �¿�S-a e`h\^�S-e�h\^Q_h=Y-a=f�e�h=^;_`^�^EÀ/VXr�eMr�^;e`rKS-m\WEZXYO[=r�^QrVba������� 3]�h\V8W�h�WQYOa/ja\S-eM�+^�S-�/e�YOV8a\^Qf��@��e`_`Y-a=r�moSU_�gqV8a\T���W�i-^Q_�gCYOa=a{moS-_`g�[\ZXY-r�V8aUe`S�W;Z8Y-[=r�^�moS-_`g�s�!�Z8^QY-_�Z8�{Yf/^�WEVXr�V8S-a��\_`SdW;^Qf/[=_�^�moS-_������� "�dVb^QZ8f\r�Yqf/^�WEVXr�V8S-an�\_`SdW;^Qf/[=_�^�moS-_���W�i-^;_`gCYOa\a r�WEZXY-r`rQs� ������� ���­~/s ���1�=���E�8��¦�¦�� � � ���O¡�ª�� Ê-���;��Ê-��ÊCªE¢��«�=�� �@¥O¤�Ê-�;¤��«¡@Ë ��C¥O¤��C¥I¤��

� @�U�E���¬¢ � � � � ® &²{�X¦(Æ�¡=�«����ÈE¥O¤��I�«��& �� �� � ��������F�� �a»v ¾U Iy�s� �akm�YUW�e YtgqS-_`^�TU^;a\^Q_`Y-Z_`^Qr�[\Z}e�V8r�Y-WEe�[=Y-ZbZ8���\_`SIc-^;akYUr������� �V8r

a\S-e�V8a@cIY-_�VXYOa@e�[\a=f\^;_ � � s��dS ������ �VXr�^EÀde`^;a=f/^�f�e�S�YtWEZXY-r`r � ]�h\VXW�hkV8r�VbadcIYO_`VXYOa@e[\a=f\^;_ � � ®o^Qc-^;a5[\a=f/^Q_�[=a\_�^�r�e`_�VXW�e`^Qfw_`^Qr�S-Z8[/e`VbSUa �{²�s���h\^Qa5Vbe�VXr r�h\SI]�ake�h=YOe�� �e�^Q_�gqV8a=YIe`^Qr�SUa � s %���;�C�I¤)(�����h\^�e`^;_`gqVba=YOe�V8S-awS-m � � SUa������� �S-a\Z8���@V8^;ZXf\r�V}e�r�f/^�WEVXf\YO�=VbZ8V}e����+^QW;Y-[=r�^� � VXr�W;S-gq�\Z8^Ee�^ P�u"[/e{e�h=^�WESUg��=Zb^;e�^;a=^Qr`r SOm���j�S-_�f/^;_`Vba=Tn_`^E�=a=^;gq^;a@e`r�V8r�Y�TU^;a\^Q_`Y-Z_`^Qr�[\Z}e�Vba5Y-[/e�SUgCYIe�^�f�f/^Qf/[�W�e�V8S-as���ZXr�Sqe`h\^��\_`SdSOmMe�h=YOe ���V8r�Vba=f\^;^Qf5YOaw��j�S-_�f/^;_`V8a\TVXr�Ð@[\Vbe�^kr�Vbgq�\Z8^-s#��h@[�rqe�h\^ke�h\^kgCYO��S-_tWESUgq�\Zb^;À/V}e��µS-m e�h\^w�\_`SdSOm ZbV8^QrtVba¸r�h\SI]�V8a\Te�^Q_�gqV8a=YIe`VbSUaKs � �e�V8r(a\SOe3��[=r�e������� �Y-a=f�e�h\^���W�i-^Q_�gCYOa=a�W;Z8YUr�r�]�h\VXW�hCW;Y-a��+^�f/^�WEVXf/^Qf��d��SU_`f\^;_`^Qf

_`^Qr�S-Z8[/e�V8S-aKs� �alm�Y-W�e e`h\^;_`^qV8r{Y��\_`SUYUfk_�YOa\TU^�S-m�e�_�Y-f\V}e`VbSUa=YOZ�YOa�f5a\^Q] W;Z8YUr�r�^Qr�]�h\VXW�hW;Y-ak�+^�f/^�WEVXf/^Qf��d�wr�SUgq^{S-_�f/^;_`Vba=TC_�^;�=a\^;gq^QaUeq®�r�^;^�vb|2�-y«²Es���a\S-e�h\^Q_�^;À\YOgq�\Z8^�V8r�e�h\^gqS-a=YUf/VXW�W;Z8YUr�r�]�h\VXW�hÃW;YOaº��^kf\^QWEVXf/^�f´cdVXYke`h\^w��j�S-_�f/^;_`Vba=T�� N f/^E��a\^Qf»V8a»�(À/Y-g�j�\Z8^ �=s �/¿1]�^�S-a=Zb��h=Y�cU^�e�S�YO�=�\Zb� � �e`Ste`h\^CWEZXYO[=r`YOZM_�^Q�\_`^Qr�^;a@e`YOe�V8S-a�� ����Â�S-m(e�h\^gqS-a=YUf/VXW{WEZXY-r`r;�� �����������������»~/s ����^Ee�� ��� ��^�e�h\^�gqS-a=YUf/VXW�WEZXY-r`rQsM��h\^Qa�� ����ÂUVXr�e�h\^ WEZXY-r`r�SOm

YOZ8Z�r�^Ee�r�S-m�WEZXYO[=r�^Qr &ÅS-�\e`YOV8a\^�f�c@VXYqe`h\^�r�e`YOa�f\YO_�fwWEZXYO[=r�^ moS-_`g�e�_�YOa=r�moS-_`gCYIe�V8S-a�mo_`S-g� ����s

Page 26: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

�OÌ )1*O,/.1)+0123,/4k*-,/687+9;:=<� ������� ���­~/s ¾�� � �Ê-���;��Ê-�E¦�������� �(���«����ÈE¥O¤��I�«��& ������� � � ® &²��X¦�Æ�¡=�«����� ��������F��V8a¹v �@��yYOa�flv ¾- Oy�s %

�������������5~/s ����K^;e�Î �+^ e�h\^{gqSUa=Y-f/VXW�moS-_`g�[\ZXY®��)� 4;²;®��)��N�²;®E�F �4E²;®E�� N;²E®H�)� Q ²E®�"C®$� 4;²�'z® ";"C®$ �4;²�< "C®$� Q ²�²�' ";"C®0��N�²�²32

��h\^Qane`h\^�WESU_�_`^Qr��+S-a=f/V8a\Tqr�^;e�SOm�WEZXYO[=r�^Qr�VXr& �+ � "C®0M/²�¿ "C®$ )4E² � "C®�K�®0 �4 %J �N;²�²�¿�"C®?>E² � � 2

�e�VXr�^QY-r��qe�SCr�^;^�e�h=YOe � � ® &² � &��/]�h\V8W�h�T-V8c-^�r�Y�e`_�V8cdV8Y-Z3�\_�SdS-mSOm�e�h\^{r`YIe�VXr���YO�\V8Z8V}e��SOm�&�s���ane`h\^{SOe`h\^;_�h�YOa=fn[\a\_`^Qr�e�_`V8WEe�^�fn_`^Qr�S-Z8[/e`VbSUanf/Sd^Qr�a=SOe�e�^Q_�gqV8a=YIe`^ S-a &�s ���SOe`^�e�h=YOe����E¤����«¡+�O�R��¥O¡qSOm�_`^Qr�S-Z8[/e`VbSUa�f/^QW;V8r�V8S-a��=_�S/WE^�f/[\_`^Qr�V8r�e`h\^ i-^;��moSU_"�=_�SIcdV8a\T

f/^�WEVXf\YO�\V8Z8V}e���S-m+W;Z8YUr�r�^QrQs�u"[/e�e�h=^�e`^;_`gqVba=YOe�V8S-a�SOm=_`^Qr�S-Z8[/e`VbSUa�_`^E�=a\^Qgq^;a@e`r�VXrMg�[=W�h�Zb^�r�rf/^Q��^Qa=f/^;a@e�SUa�e`h\^�r�VbTUa=YIe`[\_`^�S-m+�\_`S-�=Zb^QgqrMe`h=YOa�e`h\^�YO�\�=ZbVXW;Y-�\VbZ8Vbe���SOm1gqSdf\^;Z/e`h\^;SU_�^;e�VXWgq^Ee`h\S/f\r;s{��h\^Q_�^;moS-_`^�_`^Qr�S-Z8[/e�V8S-akf/^�WEVXr�V8S-ake�h\^QS-_`��Z8^QYUf\r�e`S�r�^;cU^;_�YOZr��da@e`Y-WEe�VXW�^;À@e`^;a/jr�VbSUa=r�SOm�e`h\^{e�_�Y-f\V}e`VbSUa=YOZ3��_`r�e�j�S-_�f/^;_�f\^QWEVXr�VbSUa�W;Z8YUr�r�^Qr{vb|2�-y�s�!�S-a�WE^;_`a\V8a\T�e�h\^�f/^QW;V8r�VbSUa�\_`S-�\Z8^;g·Vbe`r�^;Zbm=_`^Qr�S-Z8[/e�V8S-a�_�^;�=a\^;gq^QaUe�r�e�hd[=rMSOÇ1^;_�YOa�^;Z8^;TUY-a@ee�SdSUZUe`S��=_�SIcU^�f/^QW;V8f=YO�\V8Z}jVbe���S-m1�=_`r�e�j�S-_�f/^Q_�WEZXY-r`r�^�r;¿-e�h\^Q_�^;moS-_`^�e�h=^;�CW;Y-aC��^�WES-a�r�VXf/^;_`^QfqYUr�Y�Ë@�E¡1�E¤`�I�1�«�=��¥I¤��;�R�����O��C�E�o�\¥�Ê-¥O�b¥�Ë-¢�V8a�gCYIe`h\^;gCYOe�VXW;YOZ/Z8S-TUV8W-s��wSU_�^QSIc-^Q_e`h\^;��Y-_�^"[=r�^Emo[\Z\moS-_(r�S-Z8c@V8a\TC��¥I¡+�;¤��;���¦;�I���X¦oÆ��-ª;�«�¬�«��¢�¨1¤�¥-ª;�b�;��¦�Y-a=fqYO_`^�gqSUr�e�^Qr`r�^Qa@e�VXYOZ/e`S{e�h\^�^EÁtWEV8^;a=W;��S-m1e�h\^QS-_`^;g �=_�SIcdV8a\T�\_`S-TU_`Y-gqrQs

>��A���LF� ����P�*µP�D��/FQPRH�D ��� ������H��RLF�P�H+D�A !�[\e�j�^;Z8VbgqV8a=YIe`VbSUaµV8r�SUa\^�S-m�e�h\^�gqSUr�eV8g��+S-_�e`Y-a@e�e`^QW�h\a\VXÐ@[\^Qr�S-m��\_`S@S-m�e�_�YOa�r�moSU_�gCYIe`VbSUaKs¹��S-[=T-h\Z8�¹r��+^QY-i@V8a\T��(^;Z8VbgqV8a=YIe`Vba=TWE[\e`r"mo_`S-g$Y��\_`S@S-mT-^Qa\^;_�YIe`^Qr"Y�a=^;]Í�=_�SdSOm�]�V}e`h\S-[/e�Z8^;gqgCY-rQ�/]�h\VXW�hn^�r�r�^;a@e�VXYOZ8Z8�qW;S-a/jr�V8r�e`r�SOm+e�h\^�r��da@e`Y-WEe�VXW�gCYIe�^Q_�VXYOZ/S-m1e�h\^��\_`SIc-^Qa�e`h\^;SU_�^Qg�¿UV�s ^Us�]"^�S-�\e`YOV8aC�\_`SdSOm�rMmo[\Zb�=Z8Z}jV8a\T{e�h=^{¦�§=ª�ÈE¥O¤���§/�b��¨1¤�¥`¨=�E¤���¢Is(��_`YUf/V}e`VbSUa=YOZ8Z8��WE[\e�j�^;Z8VbgqV8a=YIe`VbSUatr�^Q_�cU^Qf�e�h\^��=[\_��+SUr�^�e`Sr�h\SI]·WES-a�r�VXr�e`^;a=W;�nS-m�W;Y-Z8W;[\ZbVMYOa=f�e`hd[=r��=Z8Y��U^QfwYtW;^;a@e�_�YOZK_`S-Z8^�V8akgq^Ee�YOgCYIe`h\^;gCYIe`V8WQr;s �a�e`h\VXre`_`YUf/Vbe�V8S-a=Y-Z@W;S-a@e�^;À@e�e�h\^�YOV8g&V8r�e`S�f/^;�=a\^���[=r�e�Y���¥O¡\¦��R¤�§=�;���«©����C�;�«�=¥QÊ�moS-_M^;Z8V8g�jV8a=YIe`Vba\TqWE[\e`rQ�@Vbe`r�YUW�e�[�YOZ1[=r�^�Y-r"YOa�YOZ8T-SU_�Vbe�h\g­VXr�S-mgqVba=S-_"Vbgq�+S-_�e`YOa�WE^-s�u"[/e�VbangqS-_`^_`^QWE^Qa@e�e`Vbgq^(�=s ��s��V8_`Y-_`fwf\^;gqS-a=r�e�_�YIe`^Qfke�h=YOe W;[/e�j�^;Z8VbgqV8a=YIe`VbSUa5SUa5_`^QYOZMgCYIe`h\^;gCYIe`V}jW;Y-Z\�\_`SdSOm�r�gCY����\_`S/f/[=W;^�c�Y-Zb[�YO�\Z8^�gqYOe�h\^QgCYIe�VXW;Y-Z\V8a/moS-_`gCYIe�V8S-awvb|Q¶Oy�s� �aC�=YO_�e�VXWE[\ZXYO_�h=^r�h\SI]�^�f3�1h\SI] Yn�\_�SdS-m(SOm�cIYOazf/^;_�'ÅYO^;_�f/^QaK r�e`h\^;SU_�^Qg [�r�V8a\T�WES-a�WE^;�\e`r�SOm(e`S-�+S-Z8S-T-�W;Y-aº�+^�e�_�YOa=r�moS-_`gq^Qf´Vba@e�S¹Y-aº^QZb^Qg�^Qa@e`YO_`�µWESUg��\V8a=YOe�S-_`VXYOZ"�\_�SdS-m��d�µgq^QYOa�rqSOm�W;[/e�j^;Z8V8g�V8a=YOe�V8S-aKs(��hd[=r�V}e"gCYOi-^�r�r�^;a�r�^�e�S�V8adc-^�r�e`VbT@YIe�^�WE[/e�j�^QZbV8gqVba=YOe�V8S-aCmoSU_�¦��«¡dËO�b�"¨+¤�¥�¥�È`¦��V8anSU_`f/^Q_�e`S�SU�/e`Y-Vba�Y-f\f\V}e`VbSUa=YOZ1gCYIe`h\^;gCYIe`V8WQYOZ+Vba\moS-_`gqYOe�V8S-anS-anY�e�h=^;S-_`^;g�s�u"[/e"e�h\^QaYOaµ�O� ËU¥O¤��«�«�/������YO�=�\_�S@Y-W�hCe`StWE[/e�j�^QZbV8gqVba�YIe�V8S-a��+^QWESUgq^Qr�gqS-_`^�Vba@e�^Q_�^�r�e`Vba=T=s��h\^�r�e`Y-a=f\YO_�f�gq^Ee`h\S/fwSOm�W;[/e�j�^;Z8VbgqV8a=YIe`VbSUawV8r�e�h�YIe�S-m���^;a@e�pQ^;akf/^;�=a\^�fwVba5h\V8r�m�YIj

gqS-[=rq¯`��Y-[\�/e`r`YIe`pQ±�v}|I��y�s���h\^�gq^;e�h\S/f�V8r�^�r�r�^;a@e`V8Y-ZbZ8�CY�a=S-a=f/^;e�^Q_�gqV8a\V8r�e�VXW YOZ8T-SU_�Vbe�h\g^EÀde`_`YUW�e�^�fkmo_`S-g h\V8rC®RWESUa=r�e`_�[�W�e�V8c-^�²��\_�SdS-m�s� �e�r�W�h=YO_�Y-WEe�^Q_�VXr�e`V8W�mo^QYOe�[\_`^qV8r{Yl¦�����¨ ��X¦;�¤���ÊI§=�;����¥I¡tS-m�W;[/e�WESUgq�\Zb^;À/V}e��Us� �a�e�h=V8r�_�^�f/[=W�e`VbSUa�e�h\^�W;[/e�moSU_�g�[\Z8YUr�YO_`^{f/^QW;S-gq��S@r�^�f]{s _Qs eQs�e`h\^;V8_�S-[/e`^;_`g�S@r�e�Z8S-T-VXW;Y-Z�SU��^Q_`YOe�SU_�®oZ8^QYUf/V8a\T�e`S�Y�f/^�WE_`^QY-r�^�S-me`h\^�Z8S-TUV8WQYOZ1WESUg�j�\Z8^EÀ/Vbe��/²EsM�kS-_`^;SIc-^Q_Q��e`h\^�WE[/e�moS-_`g�[=Z8YUrKe`S��+^�^;Z8VbgqV8a=YIe`^Qf�g�[=r�e���^�_`^;a=f/^Q_�^�f��\_`V8a=WEV8�=YOZmoS-_`g�[=Z8YUr�SOm3V8a/mo^;_`^;a=W;^Qr��d�qY-f/^�Ð@[=YIe`^��\_�SdS-m�e`_`Y-a=r�moSU_�gCYOe�V8S-a=r�®�Zb^�Y-f/V8a\T e�S�Y _�^�f/[=W�e`VbSUaSOm e`h\^5_�YOa\i\²Es ��^Qr��\Vbe�^kVbe`r�^;Z8^;TUY-a=WE^U����^;a@e�pQ^;aK rtgq^Ee`h\S/fÃV8rnYOZ8T-SU_�Vbe�h\gqVXW;Y-ZbZ8�µc-^Q_��

Page 27: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � �@�

WES@r�e`Zb��®oS-mWESU[\_`r�^�]"^�W;YOa=a\SOe��=Z8Y-g�^���^;a@e�pQ^;aK�dY-r�h\V8r�YOV8g ]�Y-r�a\SOe�e�S�f/^;�=a\^�Y-atYOZ8T-S-j_`V}e`h\gIP ²Es(��h\^�_`^QYUr�SUaCV8r�e�h�YIe"e�h\^�gq^Ee�h=Sdf�V8r�ZXYO_`T-^;Z8��Vba=f\^;�+^;a=f/^Qa@e"S-mKe�h\^ f/^Q_�V8cIYIe�V8S-a�rYOa�fnS-me`h\^C�«¡=¡1�E¤�r�e`_�[�W�e�[=_�^ SOmMe�h=^�WE[/e�moSU_�g�[\Z8YUr;s��h\^�Y�cIYOV8ZXYO�\V8ZbVbe���SOm�_�^�r�SUZb[\e�V8S-a�e�h=^;S-_`^;g �\_`SIcdVba\TtY-a=f�e�h=^�m�Y-WEe�e`h=YIe�_�^�r�SUZb[/e`VbSUawV8r

V8a�r�S-gq^{r�^;a=r�^{Yl¯`r�[=�+WQYOZXWE[\Z8[=r`±�S-m �� ®Rr�^Q^{�/^QW�e`VbSUaw¾U²�gCYOi-^�r�_�^�r�SUZb[\e�V8S-anY�a=YOe�[\_�YOZW;Y-a=f/VXf\YIe`^qVbaze�h=^CVbadc-^�r�e`VbT@YIe`VbSUa5SOm�WE[/e�j�^QZbV8gqVba�YIe�V8S-as� �aze`h\V8r�r�^�W�e�V8S-az]"^�]�V8Z8Z�Vba/moSU_�jgCYOZ8Zb���\_`^Qr�^;a@e�Y-a5YOZ8T-SU_�Vbe�h=g�VXW{gq^Ee`h\S/fwSOm��;§/� ���E�¬�«���«¡+�O�R��¥O¡µªE¢�¤��E¦E¥O�¬§/����¥I¡=�3Y-aw^EÀ\Y-WEeYOa�fw^EÀ/h=Y-[=r�e`VbcU^{e�_`^QYOe�gq^;a@e W;YOaw�+^�moSU[\a=f5Vba´v ~�y�s���h\^�_�^�r�SUZb[\e�V8S-awgq^Ee`h\S/fkr�[=�=r�e�YOa/je�VXYOZ8Z8�5f/VbÇ+^Q_`r�mo_`S-g ��^QaUe`p;^QaK r SUa\^-s� �a5e`h\^��=_`r�e�r�e`^;�ÅYnr�^Ee{S-m�WEZXYO[=r�^Qr�VXr T-^Qa\^;_�YIe`^Qfmo_`S-gÉe�h\^ f/^Q_�V8cIYIe�V8S-a�r(SOme�h\^�WE[/e"moS-_`g�[\ZXY-rQs���h\^Qr�^�r�^Ee�r�S-mWEZXYO[=r�^Qr�YO_`^�YOZ8]�Y��dr([\a=r`YIe�jVXr���Y-�\Z8^�YOa=fCe�hd[=r(h�Y�c-^�Y{_`^Qr�S-Z8[/e�V8S-aq_`^Emo[/e�YIe`VbSUaKs���h\^�WESUa=r�e�_`[=W�e`VbSUaCSOm1e�h\^�_�^�r�SUZb[\e�V8S-a_`^Emo[/e�YIe�V8S-a´V8r�e�h\^�r�^�WES-a�f¹r�e`^;�¹SOm�e`h\^��=_�S/WE^�f/[\_`^-sw��S-e�^�e�h=YOe�e�h=V8r�r�e`^;�µ_`^;�\_`^Qr�^;a@e�rY5f\Vb_`^QWEe�YO�\�=ZbVXW;YOe�V8S-a¹SOm�Y-[/e�SUgCYIe�^�fze�h\^QS-_`^;g �\_`SIcdVba\T�sw��h\^�_`^Qr�S-Z8[/e�V8S-a¹_`^Emo[\e`YIe`VbSUaS-�\e`YOV8a\^�fqmo_�SUgÉe�h\^�e�h\^QS-_`^;gÉ�\_�SIcU^;_�e`h\^;a�r�^Q_�cU^Qr(YUr�Yt¦ (U�;�b�E��¥I¡�SOmY-a �� j��\_`S@S-m3]�V}e`hS-a=Zb��YOe�SUg�VXW WE[/e�r;¿\e�h\VXr �� j��\_`S@S-m�VXr�S-�/e�YOV8a\^Qfn�d�C�=Z8ZbV8a\T�e�h=^�r�iU^;Z8^Ee�SUa�]�Vbe�h��=Y-_�e�r�SOme�h=^�SU_�V8T-V8a=Y-Z �� j��\_`SdSOm�®RY-W�e`[=YOZ8Z8��]�Vbe�hz�\_`SdSOm(�\_`SO��^�W�e�V8S-a�r`²Es���h\^�ZXY-r�e�r�e�^Q�lW;S-a=r�V8r�e`rSOmMe�h=^{^;Z8VbgqV8a=YIe`VbSUa�S-mMYOe�S-gqVXW WE[/e�r;s��Zbe�h\SU[\T-hzWE[/e�j�^QZbV8gqVba=YOe�V8S-akT@Y�c-^ e`h\^�SU_�V8T-V8a=YOZ�gqSOe�V8cIYIe`VbSUawe�S�e�h\^�f/^;cU^;Z8S-�\gq^;a@e�SOm

e�h=^�_`^Qr�S-Z8[/e�V8S-aqgq^Ee`h\S/f3�-e`h\^�Y-�\�\_`SUYUW�h�VXr�m�Y-_�gqS-_`^�T-^Qa\^;_�YOZ��V8a=f/^Q^Qf3�Ue�h\^�^;Z8VbgqV8a=YIe`VbSUaSOm"WE[/e�r�Y-�\��^�YO_�r�YUr�Y�r��+^QWEVXYOZ�W;YUr�^�SOm(_`^Qf/[\a�f\YOa=W;�@j�^QZbV8gqVba=YOe�V8S-awV8a �� j��\_`SdSOm�rQs���s T=sVbe�r�[/ÁtW;^Qr�e�h�YIeqe�h\^wZ8^Em«e�W;[/eqmoS-_`g�[\ZXYlZbSUT-VXW;YOZ8Z8�¹Vbgq�\Z8Vb^�rqe�h=^�_`V8T-h@eCS-a\^U¿�e`h\^;�ºa\^;^�fa\S-e �+^Cr��da@e`YUW�e`V8WQYOZ8Zb��^QÐ@[=Y-ZRs� �akm�YUW�e e�h\^q_`^Qr�S-Z8[/e�V8S-algq^Ee�h=SdflVXr�ZXYO_`T-^QZb�wY5¦;�E�C�I¡��R���S-a=^-s¸%\[=_�e`h\^;_`gqS-_`^ne`h\^wgq^Ee`h\S/f»WQYOa»��^wTU^;a\^Q_`Y-ZbV8p;^�f¹e`SµYlgq^;e�h\S/f»SOm S/W;WE[=_�_`^;a=W;^^;Z8V8g�V8a=YOe�V8S-aÅVba �� j��\_`SdSOm�r ]�h\VXW�hzr�h\^�f\r gqS-_`^�Z8VbTUh@e SUa5e`h\^C_`S-Z8^�S-m�_`^Qf/[=a=f\YOa�WE�wV8a�\_`SdSOm�rQs �aCe�h\^��=_�r�e�r�e`^;�t]"^�_`^Qf/[=W;^�WE[\e�j�^;Z8VbgqV8a=YIe`VbSUaCe�S{moSU_�g�[\ZXYIj�^;Z8VbgqV8a=YIe`VbSUaK�Ke`h=YIe"g�^�YOa=r

]"^Ce�_�YOa=r�moS-_`g Yw�=_�SdSOm�� ]�V}e`hµWE[/e�r�V8aUe`SkYwWE[/e�jRmo_`^;^��\_�SdS-m � S-m�Y-a¹^EÀde�^Qa=f/^�fÅ^;a=fdjr�^QÐ@[\^;a@e�¿(e�h=V8r�e�_�YOa=r�moS-_`gCYIe`VbSUaî�[\a\Z8VbiU^´¯�_�^�YOZX±wWE[/e�j�^QZbV8gqVba=YOe�V8S-a�²�V8r�h=Y-_�gqZ8^Qr`r�V8a¹e�h\^r�^;a=r�^ e�h=YOe�e�h\^ e`Vbgq^�WESUgq�\Zb^;À/V}e��nV8r�Z8Vba=^QYO_�V8a�e�h\^�r�V8p;^ SOm��"s� �����������������ºÌ\s8|���'z^�f/^;�=a\^{Y�gqY-�\�\V8a\T��������1]�h\VXW�h�e`_`Y-a=r�moS-_`gqr�Y-a �� j��\_`SdSOm �

SOm�Yqr�^�Ð@[\^;a@e � � � ��� ]�Vbe�hwWE[\e�moS-_`g�[\ZXY-r 4 %�2 2�2 � V8a@e�StY-a �� j��\_`SdSOm � � S-m��®� 4 , 4;² ' 2 2�2 'G��®� � , � ²?%�� ���

V8ane`h\^ moS-Z8Z8SI]�Vba\Tq]�Y��1�M�MYOiU^ Y-an[=�\��^Q_�gqS@r�e�W;[/e�YOa=fnVbe`r�f/^Q_�V8cIYIe`VbSUa���®�54E²

� 4 � � 4 % ®��&N�²

% ��N � � N� 4 % ��N � � 4 %�� N � ( �

S/W;W;[\_�_`V8a\TqVba �¸YOa=f�_`^;�\ZXY-W;^�Vbe��d��� Ï®� 4 ²

� 4 � � 4 % ®�� N ²

%�� N � � N , %�� 4 % � N � � 4 %�� N ,¸���

��m«e`^;_`]"Y-_`f=r�Y-�\�\Z8� �´� �«j�V8a/mo^;_`^;a=W;^Qr�e�Sne�h\^�^;a�fdj�r�^QÐ@[\^Qa@e�S-m�� Ï S-a5e�h\^�mo_`^;^�c�Y-_�VXYO�=Zb^�rV8a , $_�^�r�[\Zbe�V8a\TlVba´Y5�\_`S@S-m���Ï Ï�S-m ��®� , �²3%�� 4 %�� N � � 4 %�� N s5 �e`^;_�YIe`^Ce�h\^�\_`S/WE^Qf\[\_�^qSUale`h\^Ca\^;À@e�[=�\��^Q_�gqS@r�e�WE[\e`r e`VbZ8Z�YOZ8Z�W;[/e`r{Y-_�^q^;Z8V8g�V8a=YOe�^QfÅY-a=fzi-^;^Q�zY-ZbZ

Page 28: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

�Ox )1*O,/.1)+0123,/4k*-,/687+9;:=<SOe`h\^;_�V8a/mo^Q_�^Qa=WE^�r�[\a=W�h=Y-a\T-^�f3s���h\^ _�^�r�[=Z}e�VXr�Y��\_�SdS-m ��ÏKSOmMe�h\^�r�^QÐ@[\^QaUe � ÏK�

��®� 4 , 4 ²3%�2 2�2 ��® �� , ��\²?%� � � 2%MVba�YOZ8Zb� � � VXr�S-�/e�YOV8a\^Qf��d��W;S-a@e�_�Y-WEe�V8S-a=r�YOa�f 'º����s'l^�WQYOZ8Z3e�h\^{a=^;] r�^QÐ@[\^Qa@e � Ï3�de�h=^��E§/� ���� U���E¡=¦���¥I¡qSOm � ]{s _�s e�s ��s � �e�VXr{^QYUr��5e�S5r�^;^qe`h=YIe ��� ���R® �"²{VXr{V8a=f/^Q^Qf¹YkW;[/e�j�mo_�^Q^C�\_`S@S-m"S-m�e�h\^�W;[/e�j�^EÀde`^;a=r�VbSUa

SOm � ]{s _Qs eQs ��s���h\^{S-a=Zb��a\S-a@e`_�V8cdV8Y-Z3��SUVba@e�VXr�e�h=^��\_`^Qr�^;_`c�YOe�V8S-a�SOm�e�h=^�^;V8T-^Qa@cIY-_�VXYO�\Z8^WESUa=f/Vbe�V8S-a=rQs��m«e�^Q_(e`_`Y-a=r�moSU_�gCYOe�V8S-a�SOm+e�h\^��=_�SdSOm �µS-m � e�S ��� ����® �"²�S-m�e`h\^�W;[/e�j�^EÀde�^Qa=r�VbSUa � Ïde�h\^�\_`S-�\Z8^;g S-m�WE[\e�j�^;Z8VbgqV8a=YIe`VbSUa�V8a��°W;Y-at��^ _`^Qf/[�WE^Qfte�S�e�h\^{WESUa=r�e�_`[=W�e`VbSUatSOm�Y�WE[\e�j�mo_�^Q^

�\_`SdSOm�S-m � mo_`S-g ����� �R® ��²�st��h\^Ca=^;] �=_�SU�\Zb^Qg e�h=^;a¹WESUa=r�VXr�e`r V8a5e`h\^C^;Z8VbgqV8a=YIe`VbSUaÅSOme�h=^�moS-_`g�[=Z8Y B¹�!��® 4 , 4;² 'G2�2�2C'���® � , � ²�SUaqe�h\^�Z8^Em«e�j�h�YOa=fdj�r�V8f/^�SOm1e�h\^�^;a=fdjr�^QÐ@[\^;a@e�s�%\SU_e`^QW�h\a=V8WQYOZ-_`^QYUr�SUa=rK]"^�YUr�r�[\gq^�e�h�YIeMe�h\^�^;a=f�r�^QÐ@[\^Qa@e�SOm � V8rMr�iUS-Z8^;gqV8p;^QfKs��S-e�^�e�h=YOe �� j��=_�SdSOm�r"W;Y-at�+^�r�i-SUZb^Qg�V8p;^�fC�d�CY��+S-Z8�@a=S-gqV8Y-Z=e`_`Y-a=r�moS-_`gqYOe�V8S-atf/^;�=a\^�fV8aÅv �Oy�s��h\^���_`r�e�r�e�^Q��V8a�e�h=^�moSU_�g�[\ZXYIj�^;Z8VbgqV8a=YIe`VbSUa{�\_�S/W;^Qf/[\_`^�W;S-a=r�VXr�e�rKV8a�e�h=^"W;S-a=r�e�_`[=W�e`VbSUa

SOm�Y�r�^Ee�SOmMWEZXYO[=r�^QrQs���h\V8r�r�^Ee�WESU_�_`^Qr���SUa=f\r�e�SqY�Z8^Em«e�S/W;W;[\_`_�^Qa=WE^�SOm�Y�®ocIYOZ8VXf=²�moS-_`g�[\ZXYV8ale`h\^C^;a�fdj�r�^QÐ@[\^Qa@e S-m�Y-a �� j��=_�SdSOm�st��S-[\TUh\Zb�kr��+^QYOidV8a\T�]�^�e`_`YUWE^�e�h\^tf\^;_`VbcIYIe`VbSUaSOm�e�h\^�moS-_`g�[\ZXY>BÄ®o^Qa=WES/f/V8a\Tne�h\^qWE[\e�moSU_�g�[\Z8YUr�S-m�e�h\^qSU_�V8T-V8a=YOZ��\_`S@S-m`²��=Y-W�i�e�S�e�h\^V8a\V}e`V8Y-Z�r�^QÐ@[\^QaUe�r;sM �a�e�h\^�V8a\Vbe�VXYOZ+r�^�ÐU[=^;a@e`r�]"^�r�^Q�=YO_�YIe`^�e`h\^��=Y-_�e�r�]�h\VXW�hqY-_�^�Y-a=WE^�r�e`S-_�rSOm B Y-a=f�S-�/e�YOV8awYCr�^;e�SOm(WEZXYO[=r�^Qr#&z]�h\^;_`^{^QYUW�h � � &lVXr�SOmMe�h\^�moS-_`g � �� � � � S-_# � �s���S-V8a\T�f\SI]�aCVbaCe`h\^��=_�SdSOm3]"^�Z8S@SUi�]�h=^Ee�h=^;_�e�h\^�WES-_`_`^Qr���SUa=f/V8a\T{Vba\mo^;_`^;a=W;^]"S-_`idr�S-akYOa�WE^Qr�e�SU_`r�SOm-B SU_�a\S-eQs� �a�e`h\^��=_�r�e�W;YUr�^�]"^�h=Y�cU^{e�Snr�[\�\��^QW�e�e�h\^�r�^;e`r�SOmWEZXYO[�r�^�r�e�SC[\a=VbSUaK�\V8ane`h\^�r�^QW;S-a=fnS-a\^ e`StYq�\_`Sdf\[=W�e�s���h\^{moSU_�gCYOZKf\^E�=a\Vbe�V8S-a�VXr�T-V8c-^Qa�+^;Z8SI]{�� �����������������ºÌ\s ����^Ee �Í�+^�YtW;[/e�j�mo_�^Q^��\_`SdSOm�SOm � Y-a=f � ��^�YOawS/W;W;[\_`_�^Qa=WE^{S-m�YmoS-_`g�[=Z8Y�V8a � s�'l^�f/^;�=a\^�e�h=^�r�^;e�SOm��`�=�I¤��U�E���E¤��X¦������q�E�b�O§d¦;��¦�!"��® ��% � ²�V8a=f/[=WEe�V8c-^;Z8�1��K^;e � ��^�Y-aÅSdWQWE[\_`_`^;a=W;^�S-m�Ywr�^QÐ@[\^Qa@e � Ï�V8a ��¿��d�Ã�O¡+�Q® � % � ²{]"^tf/^Qa\SOe`^qe�h\^�r�[\�/jr�^QÐ@[\^;a@e � Ï ÏS-m � Ï]�h=V8W�hkW;S-a=r�V8r�e`r�^EÀ\Y-WEe�Z8�nS-m�e�h\^�moS-_`g�[\ZXY-r�]�V}e`hkS/W;W;[\_�_`^;a�WE^Qr���^QVba=TYOa�WE^Qr�e�SU_`r�SOmKe`h\^�SdWQWE[\_`_`^;a=W;^ � Vba � s��K^Ee � �+^�e`h\^�S/WQWE[\_`_�^Qa=WE^�SOm�Y-atVba=V}e`V8Y-Z1r�^QÐ@[\^Qa@e

� V8a �ÍY-a=f � 4q® � N�²��+^{e�h\^�Zb^;m«e�®�_�V8T-h@e�²�SdWQWE[\_`_`^;a=W;^{SOm V8a � �s� �m(a\^QV}e`h\^;_� 4�a\S-_ � N�V8r"YOa�Y-a=WE^�r�e`S-_�SOm � e�h\^Qa &��!� � �U¿U �m��S-e�h � 4�Y-a=f � N�YO_`^�YOa�WE^Qr�e�SU_`r�SOm �e�h=^;a�&��!���\s(��e`h\^;_`]�VXr�^�®�^EÀ\Y-WEe�Z8��SUa\^�SOm � 4O� � N�VXr�Y-a=WE^�r�e`S-_(S-m � ²�&��!� /�I¡1�;® � % � ² �U�V�s ^Us�&�� � � �{Vbm � 4�VXr�Y-a=WE^�r�e`S-_�SOm � YOa�f &��!� � ��V}m � N VXr�YOa=W;^Qr�e�S-_�S-m � s�K^;e�[=r�YUr�r�[\gq^�e�h=YOe{e�h\^tW;Z8Y-[=r�^Cr�^Ee�r &��kYO_`^qY-Zb_`^QYUf/�kWESUa=r�e�_`[=W�e`^Qf5moS-_�YOZ8Z(r�^QÐ@[\^;a@e�¼S/W;W;[\_�_`^;a�WE^Qr �tV8a �´]�Vbe�hzÊ-��¨+�o�\® ��² � ,�®o]�h=^;_`^�e�h=^�f/^Q�/e�htS-mKYOatS/W;W;[\_`_�^Qa=WE^ ��V8r(e�h\^Z8^;a\T-e�h�SOmMe�h\^{��YIe�h�V8ane`h\^{�\_`SdSOme`_�^Q^�mo_�SUg e�h=^{_�SdSOe�e`S �+²�s��SI]¹Z8^Ee ���+^�Y-a�S/W;W;[\_�_`^;a�WE^(]�Vbe�h�Ê-��¨+�o�\® ��² � , ��|-s'z^�f/V8r�e�V8a\TU[\V8r�h{e`h\^�moSUZbZ8SI]�V8a\T

W;YUr�^�r;���� �zV8r�e`h\^CWES-a�r�^�ÐU[=^;a@e�S-m ���3V�s ^Us�Y�[=a=YO_`��_�[\Z8^qYO�\�\Z8V8^Qfwe`S �ºT-V8c-^�r��s���^Q_�^�]"^r�Vbgq�\Z8��f/^;�=a\^ & � � &��+s

� � �lVXr�e`h\^qWES-a�r�^�ÐU[=^;a@e�S-m � 4 Y-a=f � N �3VRs ^-s�Y��\V8a=YO_`��_�[\Z8^� YO�\�=ZbV8^Qfke�S � 4 Y-a=f� N T-V8c-^�r �Ks�"? � ��h\^wYO[\ÀdV8Z8V8Y-_��ÅmoSU_�g�[\Z8YUr�SOm� YO_`^wYOa=W;^Qr�e�SU_`r�SOm � ��V�s ^Usºe`h\^�moS-_`g�[=Z8YUrS/W;W;[\_�Vbaµ�O¡+��® � 4 % � ²?%��O¡+��® � N % � ²�s���h=^;a & � � &���� ��&�� Is

Page 29: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � �-¶

� ��� ��h\^�Y-[/À/VbZ8VXYO_`��moSU_�g�[\Z8YUr�SOm� Y-_�^�a\SOe YOa=W;^Qr�e�S-_�r�S-m � s� �ake�h\VXr�WQY-r�^�]"^f/^;�=a\^ & � � &������ &�� ]�h\^;_`^ �" 4 � �. 4 % 2�2 2 �" � � �.!� ��� �� 4 � �� 4 %�2 2�2 �� � � ���� ��� �" ) % �� � � �. ) % �� � 6 + � � % �� �/�

%MVba�YOZ8Zb�n!"��® ��% � ²�VXr�r�^Ee"e�S�&��{]�h\^Q_�^��CVXr�e`h\^�SdWQWE[\_`_`^;a=W;^�SOmKe`h\^�^;a=fdj�r�^QÐ@[\^;a@e�s���SOe`^e�h�YIe � VXr�YOa�S/W;W;[\_�_`^;a�WE^�Vba���YOa=f�Vbe`r�SI]�a�YOa=W;^Qr�e�SU_Qs ��������������kÌ\s8|����K^;e �Å�+^"e�h\^��\_`SdSOm®«moSU_5(&%J*�mo_�^Q^�cIYO_`VXYO�\Z8^QrQ� M{Y�W;S-a=r�e`Y-a@e�r��dg��+S-Z«²

� 4 � N®E�F�+²;®0"C®$�1²-,/.C®0�+²�² � ®��) \²E®�"C®0M/²-,/.t®$ \²�² �;§/�

]�h\^Q_�^ �-4�V8r�e�h\^ �� j��\_`SdSOm��"C®0(1² � � "C®0(1² .t®$(3² � .t®$(3² �"C®0(1² � %J"C®$(3²5, .C®0(1² � .C®0(1² � ,°�5�

"C®$(3² ,/.C®$(3² � ®0"C®0(1² ,/.t®$(3²�² � ,¸���

"C®$(3² ,/.C®$(3² � ®��) \²;®0"C®$(3² ,/.C®0 \²�² � �n���®����1²E®0"C®0�+²-, .C®$�1²�² � ®��! /²;®0"C®0(1² , .C®$ \²�² � �5���

®E���1²E®�"C®$�+² ,/.C®$�1²�² � ®����+²;®��) \²;®0"C®$�1²-, .t®$ \²�² � �5� �

YOa=f �5N V8rQ�"C®0M/² � "C®0M/² � .C®0*d² � � .C®$*/²"C®0M/²?%�®0"C®�Md² ,/.C®$*/²�² � � .C®$*/² ,°�5�®0"C®0M/² ,/.t®$*/²�² � � "C®0M/²-,/.C®0*d² ,¸���

®0"C®0M/²-, .C®$*/²�² � � ®��) \²E®�"C®0M/²-, .C®$ \²�² �n� �®H�) \²E®0"C®�M/²-,/.C®0 /²�² � � ®H�) \²E®0"C®�M/²-,/.C®0 /²�² ��� �

®E�F�+²;®��) \²E®�"C®$�1²-, .C®0 \²�² � � ®H�) \²E®�"C®0M/²-,/.C®0 \²�² �k�����h\^�Y-a=WE^�r�e`S-_�r1SOm/e�h=^�WE[/e�moS-_`g�[\ZXY�V8a �-4�YOa�f �;N�YO_`^�gCYO_`i-^Qf��d��ds�%=_�SUg �5]�^�W;S-a/j

r�e�_`[=W�e�e`h\^�W;[/e�j�^EÀde`^;a=r�VbSUa ��ÏR��]�h\^Q_�^ f/^;a\S-e�^�r�e�h=^�WE[/e�moS-_`g�[\ZXYw®E�F�+²;®��) \²E®�"C®$�1² ,.C®0 /²�²"SOm ���

�-4 �5N =, %Q®����1²E®0"C®0�+² ,/.C®$�1²�² � ®H�) \²E®0"C®�M/²-,/.C®0 /²�² ,°���

�K^Ee � �+^�e`h\^�S/WQWE[\_`_�^Qa=WE^�SOm 7, Vbake�h\^�^;a=fkr�^QÐ@[\^Qa@e � Ï SOm � Ï s�'z^�W;S-gq�\[/e`^e�h=^�W�h=YO_�Y-WEe�^;_`VXr�e`V8W�WEZXYO[=r�^Qr�!"��® ��ÏH% � ²E�%\_`S-g e`h\^��j�gCYO_`idr�V8a5e`h\^q�\_�SdS-m�r�� 4 YOa=f � N ®�]�h\VXW�hlV8a=f/VXW;YOe�^�e�h\^CY-a=WE^�r�e`S-_�r�SOm � ²]"^ �=_`r�e�T-^;e"e`h\^�r�^Ee`r�SOmMW;Z8Y-[=r�^Qr�WESU_�_`^Qr��+S-a=f/V8a\T�e�S�e�h=^{Vba\Vbe�VXYOZ�r�^�ÐU[=^;a@e`rQ�

&�4 � "C®$(3² � � %#&�N � � .C®0(1² � %#& Q � � "C®�M/² � %#& � � .C®0*d² � ��2��h\^��=_�r�etVba/mo^Q_�^Qa=WE^wV8a � 4 ®oVbe�VXr>,°���R²�e�YOiU^Qrq�\ZXY-W;^�SUaÃa\S-a=Y-a=WE^�r�e`S-_�r�SOm � ¼¹e�h\^YO[\ÀdV8Z8V8Y-_���moS-_`g�[=Z8YUr�S-mKe�h\^ V8a/mo^;_`^;a�WE^ YO_`^�a\S-e"gCYO_`i-^�fC�d���ds�!�S-a�r�^�ÐU[=^;a@e�Z8�q]�^ YO�\�=Zb��ÉYOa�f�S-�/e�YOV8a�e�h\^�r�^;e & 4 � N � "C®0(1² � .C®0(1² �Us���h\^�moS-Z8ZbSI]�V8a\TCV8a/mo^;_`^;a�WE^Qr�Vba�� 4 YO_`^YOZ8ZK[\a�YO_`�tYOa=f�r�S�]"^ S-�/e�YOV8a

!"��® �-4 % � 4Q² � "C®$(3² � .C®0(1² �moS-_ � 4 �+^;V8a\T�e�h\^{S/WQWE[\_`_�^Qa=WE^�SOmMe�h=^�YOa=W;^Qr�e�S-_�S-m � V8a�e�h\^{^Qa=fdj�r�^�Ð@[\^;a@e�SOm � 4 s

Page 30: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

¾-  )1*O,/.1)+0123,/4k*-,/687+9;:=<��h\^z�=_`r�enV8a/mo^Q_�^Qa=WE^zVba � N e�YOiU^Qrn�\Z8YUWE^zS-aÍY-a=WE^�r�e`S-_�r�S-m � ®«e`h\^¹YO[/À/V8ZbVXYO_`�»moS-_�j

g�[=Z8YUr�Y-_�^ ��j�^Qf=²�YOa=fµ]�^�h=Y�c-^te�SÅYO�\�\Z8�ze�h\^ �&SUa/&�Q % & � sÅ'l^�S-�/e�YOV8a/&�Q � � � �"C®0M/²3% .C®0*d² � �@s��VbiU^�Vba�� 4 YOZ8ZKmoSUZbZ8SI]�V8a\TtV8a/mo^;_`^;a=W;^Qr�Vba�� N YO_`^�[\a=Y-_���Z8^QY�cdV8a\Tqe�h\^r�^Ee�S-m�W;Z8Y-[=r�^�r�[\a=W�h=Y-a\T-^�f3s��^Ee � N{��^ e`h\^�Y-a=WE^�r�e`S-_�SOm � V8a�e�h\^{^Qa=fdj�r�^�Ð@[\^;a@e�SOm �5N-s��h\^Qane`h\^�WESU_�_`^Qr��+S-a=f/V8a\Tqr�^;e�SOm�WEZXYO[=r�^Qr�VXr

!"��® �5N % � N�² � � "C®�M/²?%�.t®$*/² � � 2��h\^�Z8YUr�e�V8a/mo^;_`^;a=W;^ ,¸����Vba ��Ï�e`Y-i-^Qr��\ZXY-W;^�S-a�YOa=W;^Qr�e�SU_`r�SOm � YOa�fC]�^�h=Y�cU^�e�SqYO�\�=Zb��´S-a &�4 � N YOa�f�& Q � � s(��h\VXr�^;cU^;a@e�[�YOZ8Zb�t�dV8^;ZXf\r

!"��® � Ï % � ²�� "C®$(3² � .C®0(1²3% � "C®0M/²3%�.C®0*d² � � 2�� �e�VXr�^QYUr���e`S�cU^;_`V}mo�qe`h=YIe"e�h=^ r�^Ee�S-m�W�h=YO_�Y-WEe�^Q_�VXr�e`V8W�WEZXYO[=r�^Qr�!"��® ��ÏH% � ²"WESUa=r�e`_�[�W�e�^�f

V8aÅe�h\^C^;À/Y-gq�\Zb^tY-��SIcU^�VXr{[\a�r�YOe�VXr���Y-�\Z8^-s���h\VXr{VXr a\SOe�gq^Q_�^QZb�zY�W;S-V8a=WEVXf/^Qa=WE^U��\[/e�YT-^Qa\^;_�YOZ3�=_�V8a=WEV8�\Z8^ ^EÀ/�\_`^Qr`r�^�f�V8a�e`h\^{a\^;À@e��=_�SU��S@r�Vbe�V8S-aKs �������� � ���������µÌ=sb|)�����E� �­ª`�q���E§/� �¬È�¤�����¨+¤�¥�¥�È�¥�È��o�\��¦;���E§=�;¡=� � �I¡1Ê � ª����t�8��È�� �¥��`�;§/¤�¤��;¡+���C¥�È���©��O�¬��Ê ÈE¥I¤���§/�b�w¥����E§/¤�¤��«¡dË��«¡ � � �1�=�E¡¹�o�\��¦;�E��¥�È��;�b�O§d¦E�E¦ !"��® ��% � ²�X¦�§/¡\¦;�O�R�X¦oÆ��UªE�8��� ��������F��V8alv �Oy�s�u"YUr�VXW;Y-ZbZ8��V}e�V8r"r�h\SI]�aqe�h=YOe B � �UmoSU_ B S/W;W;[\_�_`V8a\T�YIe � �3®�]�h\V8W�hnV8r

YOa�[\a=r`YIe`V8r���Y-�\Zb^"r�^�Ð@[\^;a@e�²�VXr�f/^;_`VbcIY-�\Zb^"V8a �� mo_`S-g&e�h=^"V8a\Vbe�VXYOZ\YOÀdV8S-gCr�!"��® ��% � ²�s %���;�C�I¤)(��µ��h\^l�\_�SdS-m�SOm��(_`S-�+SUr�V}e`VbSUa¸Ì\s8|kgqVbTUh@e�r�[\T-TU^Qr�eCe�h=YOene`h\^lr�^Ee�SOm�WEZXYO[�r�^�r!"��® ��% � ²�V8r���[=r�e�YtW;Z8Y-[=r`YOZa=S-_`gqY-ZKmoSU_�g SOm�e`h\^�moSU_�g�[\Z8Y�";B$WESU_�_`^Qr��+S-a=f/V8a\Tqe`SCe�h\^r�^QÐ@[\^;a@e�B � ¿=�\[\e�e�h\VXr�VXr�a=SOe�e�h=^�W;YUr�^ P���r�YCr�V8gq�\Z8^�WESU[\a@e�^;_`^EÀ\Y-g��=Zb^{WESUa=r�V8f/^Q_�e�h\^moS-Z8Z8SI]�Vba\TCf/^Q_�V8cIYIe`VbSUa ���

.C®?>E² � .C®:>;²� .t®:>E² ,/.t®:>E² ,°� �

"C®0M/² , "C®�Md² � .C®?>E² ,/.C®?>E² �·�����h\^�S-a=Zb�µV8a\Vbe�VXYOZ�r�^QÐ@[\^;a@eCSOm � VXr .C®?>E² � .C®:>E²Esº��^;Vbe�h\^Q_qe�h\^�Z8^Em«e�j�a=S-_�e�h\^�_`VbTUh@eS/W;W;[\_�_`^;a�WE^�SOm .C®:>E²�V8a�e`h\VXr�r�^�Ð@[\^;a@e�V8r�Y-a�Y-a=WE^�r�e`S-_�SOm�e�h\^{S/WQWE[\_`_�^Qa=WE^ � S-m+"C®0M/²-,"C®0M/²�V8aze�h\^C^Qa=flr�^QÐ@[\^Qa@eQsC��hd[=r�e�h\^tr�^Ee{S-m�W;Z8Y-[=r�^�r &ºWESU_�_`^Qr���SUa=f/V8a\Tne�S�e�h\^Ca=Sdf\^SOm�e�h\^lVba\Vbe�VXYOZ{r�^QÐ@[\^QaUenV8r� � �Us ��rte`h\^;_`^lY-_�^lS-a\Z8�º[=a=YO_`�Ã_�[\Z8^Qr�Vba �$]"^k�=a�YOZ8Zb�S-�\e`YOV8an!"��® ��% � ² � & � � �@s���aqe`h\^�S-e�h\^Q_�h=Y-a=fqa\S{e`_`YUf/V}e`VbSUa=YOZ\e�_�YOa=r�moS-_`gCYIe�V8S-a�e`Sa\SU_�gCYOZUmoS-_`g ®oZ8VbiU^�r�e`Y-a=f\YO_�fdj+S-_�r�e�_`[=WEe�[\_�YOZUe�_�YOa=r�moS-_`gCYIe`VbSUa�²+e�_�YOa�r�moSU_�gCr3e`h\^�moS-_`g�[\ZXY"�®0"C®�M/²�, "C®0M/²�²�V8a@e�S+ � �@s� �a5��YO_�e�VXWE[\ZXYO_�e�h\^qr�e�YOa=f=YO_�f�e�_�YOa=r�moS-_`gCYIe`VbSUawT-V8c-^Qr�e�h\^r�^Ee�S-m�W;Z8Y-[=r�^Qr��´�� � "C®0M/²3%�"C®0M/² � �Us���h\^�^EÀ\Y-g��=Zb^�Y-��SIcU^�V8Z8Zb[=r�e�_�YIe`^Qr�e`h=YIe�e�h\^�r�^;eSOm�WEZXYO[�r�^�r�!"��® ��% � ²{r�e�_`S-a\TUZb�kf/^Q��^Qa=f\r�S-ale�h\^tf/^Q_�V8cIYIe`VbSUa � Y-a=fla\SOe�SUa\Zb�lS-ale�h\^moS-_`g SOm�e`h\^�moSU_�g�[\ZXYCS-ak�+SUr�Vbe�V8S-a � P�'z^�]�V8Z8Z�r�^;^�Vbake�h\^�moS-Z8ZbSI]�V8a\Tt�=_�^�r�^QaUe�YIe`VbSUawSOme�h=^�gq^Ee`h\S/f�e�h�YIe�e`h\^�W;S-a=r�e�_`[=WEe�V8S-akS-m�!"��® ��% � ²�mo_`S-g e�h=^��\_`SdSOm �Í�\ZXY��/r�YnWE^;a@e`_`Y-Z_`S-Z8^�V8aze�h\^Cr�SOj�W;YOZ8Z8^Qfk�=_�SdSOm��\_�S-��^QWEe�V8S-aº®�]�h\VXW�hzWQYOa\a\S-e{��^q�+^;_�moS-_`g�^�fkSUa5e`h\^q�=Y-r�V8rSOm�S-_�f/V8a=YO_`�tWEZXYO[�r�^�moS-_`gCr`²Es ���SI]¸Z8^Ee�!"��® ��% � ²���^�e`h\^�®�[\a=r`YIe`V8r���YO�=Zb^�²�r�^Ee�SOm�W;Z8Y-[=r�^Qr�^EÀde�_�Y-WEe�^Qftmo_�SUgÉe�h\^ �� j

�\_`SdSOm3SOm1e�h=^�^EÀde�^Qa=f/^�fCr�^�ÐU[=^;a@e � s�u"��e`h\^�WESUgq�\Zb^;e�^Qa\^Qr`r(S-m+e`h\^�_`^Qr�S-Z8[/e�V8S-aq�\_`V8a=WEV8�\Z8^e�h=^;_`^�^;À/V8r�e`rqYl_�^�r�SUZb[/e`VbSUa´_`^Emo[/e�YIe`VbSUa ' ®oV8a´moSU_�g SOm�Y5e�_`^;^�²�S-m�e�h=^�r�^EeCS-m�WEZXYO[�r�^�r!"��® ��% � ²Es ' W;Y-a��+^ e�_�YOa�r�moSU_�gq^Qf�Vba@e`SqYqTU_�SU[\a=f�_�^;mo[/e`YOe�V8S-a�SOm(!"��® ��% � ²��

Page 31: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � ¾=|

�������� � ���������µÌ=s �������E� ' ª��t�n��¤�����¤`��¦;¥I�}§/�R��¥O¡z¤`��È�§/���I����¥I¡´¥�È��n¦;�E��¥�È��;�b�I§d¦;�E¦ & ��1�\�;¡5�o�\�;¤���� U�X¦���¦{��ËO¤`¥I§/¡+ÊC�«¡\¦����O¡+��� ' Ï�¥�È ' ¦ �8� � ' Ï(�X¦{�q��¤����{¤`��¦;¥I�}§/�R��¥O¡w¤���È�§/���I����¥I¡¥�È &3Ï ��\�;¤�� &KÏ��X¦��q¦;�;�"¥�È�ËO¤`¥I§/¡+Êt�«¡\¦����I¡+���E¦�È�¤`¥I� &�� ��������F���^Ee��k��^{e`h\^�r�Vbg�[\Zbe`YOa=^;S-[�r�gqSUr�e�T-^;a=^;_�YOZK[\a=V}�=^Q_�SOm(Y-ZbZ3e`h\^�_`^Qr�S-Z8[/e�V8S-a�r

V8a ' s���h\^Qa ' �5VXr{YOZXr�SnYn_�^�r�SUZb[/e`VbSUak_`^Emo[/e�YIe�V8S-al]�h\^;_`^�e�h\^�_�^�r�SUZb[\e�V8S-ak_`[\Z8^�_`^Qf/[�WE^Qre�SwYOe�S-gqVXW�W;[/e{YOa=fzWESUaUe`_`YUW�e`VbSUa=r�®�VRs ^-s�e�S�Y�gqVbÀ1��r�^Q^�vb|���y«²Es��K^Ee �´��^CYOazYO_`�\Vbe�_�YO_`�T-_`S-[=a=fCr�[=�=r�e`V}e`[/e�V8S-a�SOm1e�h\^�cIYO_`V8Y-�\Zb^�r(S-m ' �¿Ue`h\^;a ' Ï;� ' � ��VXr�e�h=^�f/^�r�V8_�^�fq_�^�r�SUZb[\e�V8S-a_`^Emo[/e�YIe�V8S-as %���;�C�I¤)(���'l^�WQYOZ8Z/e�h=^�_�^;mo[/e`YOe�V8S-a ' Ï=f/^;�=a\^QfqY-��SIcU^�Y TU_�SU[\a=f�_`^Emo[/e�YIe�V8S-ak��¥I¤�¤`��¦�¨=¥I¡+Ê ��«¡@Ë���¥ ' s ���SI]$Z8^Ee ' Ï���^kYlT-_`S-[=a=fµ_`^Emo[/e�YIe`VbSUa»W;S-_`_�^�r��+S-a=f\Vba\T5e�S¹Yz_�^�r�SUZb[\e�V8S-a´_`^Emo[\e`YIe`VbSUa

' S-m�!"�(® ��% � ²Esnu"�kS-[=_�f/^E�=a=V}e`VbSUazS-m"_`^Qr�S-Z8[/e`VbSUa ' Ï�W;Y-az^�Y-r�VbZ8�we`_`Y-a=r�moSU_�gq^�fwe�SkY-a �� j��\_`SdSOm�S-m � mo_`S-g &KÏ�]�Vbe�h¹YIe`S-gqVXW�W;[/e`rQsC �a=f/^Q^Qf3��S-a\Z8�5YUf\f/Vbe�V8S-a=Y-Z(WES-a@e`_`YUW�e�V8S-a�rYO_`^qa\^QW;^Qr`r�Y-_���e`Skr�V8g�[=Z8YOe�^qm�Y-WEe�SU_�V8a\T=sC��h\^C_`^Qr�[\Zbe�V8a\T �� j��\_`S@S-m ' Ï�]�V8ZbZ�r�^;_`c-^CYUr{Y¦)(-�;�b�;��¥O¡nS-m�YOa �� j��=_�SdSOm zS-m � � � ]�Vbe�hzYIe�SUgqV8W�WE[/e�r;s���^QWQYOZ8Ze`h=YIe � gCY��n�+^qYWE[\e�j�^EÀde�^Qa=r�V8S-a B>%�� ��� SOm � ��� s��h@[�r CWESU_�_`^Qr���SUa=f\r�®ogqS/f/[\Z8S�e`h\^"e�_�YOa=r�moS-_`gCYIe`VbSUa �������X²Ke`S�Y�_`^Qf/[=WEe�V8S-a�SOm�Y��\_`SdSOm

]�Vbe�hÅWE[/e�r�e�SwY��=_�SdSOm�]�V}e`hzYOe�S-gqVXW�W;[/e`rQs���h=^qW;S-a=r�e�_`[=WEe�V8S-akS-m zmo_`S-g ' Ï�V8r��=YUr�^�fS-aÅr�S�WQYOZ8Zb^�f�¨+¤`¥��;���E����¥I¡=¦�_`^;�\ZXY-W;Vba=Tte�h=^��=_�SdSOm � S-m�e�h=^qW;[/e�j�^EÀde`^;a=r�VbSUa � �@�w�=_�SdSOm�r��v � y�S-m �" %�� ��� % �. moSU_�WEZXYO[=r�^Qr � � �" � �. V8a &KÏ��K]�h=^;_`^�&KÏ�VXr�e�h\^tr�^Ee{S-m"TU_�SU[\a=fV8a=r�e�YOa=W;^Qr�_�^;mo[/e�^�f¹�d� ' Ï�sl��h\^t^EÀ/VXr�e`^;a=W;^tSOm�r�[=W�h¹�\_`SO��^�W�e`VbSUa=r{SOm � ]{s _�s e�s5WEZXYO[�r�^�rV8a &KÏ��MT-[=Y-_`Y-a@e�^;^�fz�@�le�h=^tZb^QgqgqYk��^QZbSI]{�MV8r�e�h\^ngqSUr�e�Vbgq�+S-_�e`Y-aUe��=_�SU��^Q_�e��lSOm�e�h\^WE[\e�j�^;Z8VbgqV8a=YIe`VbSUa�gq^;e�h\S/f��=Y-r�^QfnS-a�_`^Qr�S-Z8[/e�V8S-aKs�-����� �»Ì\s8|������;� � ª������;§/� �¬È�¤�����¨+¤`¥Q¥�È�¥�È��t¦;���;§=�E¡�� � ��B>%�� ��� ¦ �8� � � � � �X¦

¦)(-¥O�b�;���b£���Ê � B �X¦C©I�I�¬��Êz�I¡1Ê � �X¦q�o�\��¥��`�;§/¤�¤��;¡+����¥�È B �«¡ � � ���E� � � �" � �. ª�����;�b�I§d¦;���«¡k!"��® ��% � ²(� �1�\�;¡l�o�\�;¤��C� U�X¦��R¦����E§/� �¬È�¤�����¨1¤�¥�¥�È ��v � y�¥�È �" %� � � % �. ��«�«���® ��v � y«² � ��® �"²�� ��=�E¤�����Ê-�;¡+¥I���E¦��o�\� �8�E¡dËO�o�w¥�È��o�\��¨+¤�¥�¥�È �(���«�����«�=�{¡=§/�Cª��E¤ ¥�È�¡+¥�Ê-�E¦¥��`�;§/¤�¤��«¡@Ë��«¡5�o�\��Ê-�;¤��«©I�I����¥I¡Å�R¤`�`��� � ��������F��'z^{S-a\Z8�tTUVbcU^ Y��\_`SdSOm�r�iU^Ee`W�h¿\Y�mo[=ZbZmoS-_`gqY-Z1�\_�SdS-mMW;Y-a���^ moSU[\a=f�VbaÅv ~�y�s��h\^��\_`SdSOm�T-Sd^�r��d�lV8a=f/[�W�e�V8S-a´S-aÅe�h=^nf/^Q�/e�hµS-m�Vba\mo^;_`^;a=W;^ta\S/f/^Qr�V8a ��sk �aµW;S-a/j

r�e�_`[=W�e`Vba\T ��v � y"]�^tr�idVb�µY-ZbZ�Vba/mo^Q_�^Qa=WE^�r{V8a �·Zb^�Y-f/V8a\T�e�S�e`h\^t^;À@e`^;a=r�V8S-azmoS-_`g�[\ZXYIBts �a�e�h\^�SOe�h=^;_�V8a/mo^;_`^;a=W;^Qr�]�Vbe�hkY-[/À/VbZ8V8Y-_��qmoSU_�g�[\ZXY-r�]�h\VXW�h�Y-_�^ a\S-e�YOa=W;^Qr�e�SU_`r"SOm5B­]"^r�^;Z8^QW�e"e�]"S�WEZXYO[�r�^�r�mo_`S-g­e�h=^�W;S-_`_�^�r��+S-a=f\Vba\T�r�^Ee�SOmW;Z8Y-[=r�^Qr"YOa=fnWES-a�r�e`_�[=WEe�e`h\^�W;S-_`_�^;jr���SUa=f/V8a\Tt�\_`SO��^�W�e�V8S-a�r�c@VXY�e�h=^�Vba�f/[=W�e`VbSUakhd�d��S-e�h\^�r�VXr;s�'l^�WES-a�WE^;a@e`_`YOe�^{S-awYq�\V8a=Y-_��V8a/mo^;_`^;a=W;^{_�[=Zb^ 5Y-a=fte`h\^ moS-Z8Z8SI]�Vba\T��\_`SdSOm ���

®�� 4 ²® � 4 ² � 4 ��� 4

®�� N ²® � N ² � N ��� N

® �+² ��Ï 4 %���Ï N ��� Ï 4 % � ÏN ]�h\^Q_�^ �&4 % ��N % �ÅYO_`^�e`h\^qa\S/f/^Qr V8a5e`h\^q�\_`S@S-m(e�_`^;^ �&YOa=f �" � �. V8r{Y�WEZXYO[=r�^�Vba & �=s'z^ YUr�r�[\gq^�e`h=YIe"e�h=^ Y-[/À/VbZ8VXYO_`��moSU_�g�[\Z8YUr�S-m� Y-_�^�a\SOe�YOa=W;^Qr�e�SU_`r�SOm � Y-a=fCe`h=YIe"e�h\^r�[\�=r�^QÐ@[\^;a@e�r�S-m � ) � � ) f/^;�=a\^Qfµ�@�zmoSU_�g�[\Z8YUr�]�h\VXW�h´Y-_�^ta=SOe�Y-a=WE^�r�e`S-_�r�SOm�B YO_`^� ) � � ) moS-_*+/� |�%��/s���h\^;aK�/�d����^E�=a\Vbe�V8S-a�Ì\s �/�d]"^�h�Y�c-^ & � � &���� � &�� Is(��h\^Q_�^;moS-_`^e�h=^;_`^�YO_`^�W;Z8Y-[=r�^�r �";4 � �. 4 � & � ��YOa=f �"+N � �. N ��& � {rQs e�s

�" � �. � �" 4 % �" N � �. 4 % �. N 2

Page 32: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

¾U� )1*O,/.1)+0123,/4k*-,/687+9;:=<u"��V8a=f/[�W�e�V8S-a�h@�d�+SOe`h\^Qr�V8rK]�^(SU�/e`Y-Vba{�=_�SdSOm�r �@Ï 4 S-m �" 4 %�� 4 � � 4 % �. 4 Y-a=f �@ÏN SOm �" N %�� N �� N % �. N ]�V}e`h&��®��@Ï 4 ² � ��®�� 4 ²�Y-a=f ��®��@ÏN ² � ��®�� N ²�s���h\^Qa�e�h\^��\_�S-��^QWEe�V8S-awWESU_�_`^Qr���SUa=f/V8a\Te�Sqe`h\^{a\S/f/^ ��VXr ��ÏR�

®��dÏ 4 ²�" 4 % � 4 � � 4 % �. 4®��dÏN ²�" N %�� N � � N % �. N

�" 4 % �" N %���Ï 4 %���ÏN � �"Ï 4 %���ÏN % �. 4 % �. N !�Z8^QYO_`Z8����®���ÏX² � ��®�M²Es %���;�C�I¤)(���%=S-_"e�h\^ �\_`SO��^�W�e`VbSUa=r ��v � y]�^ a\^Q^Qf�e�h\^{r�^Ee�SOm�WEZXYO[=r�^�!"��® ��% � ²�Y-r�f/^;�=a\^�fV8a ��^;�=a\Vbe�V8S-akÌ\s �/s���^;_`^{Vbe�V8r�V8gq��SU_�e�YOa@e�e�h�YIe & �+!"�(® ��% � ²�VXr�W;S-a=r�e�_`[=W�e`^QfqÈ�¤�¥O���o�\�¨+¤`¥Q¥�È �µV}e�r�^QZ}m P(��h@[�r�&�VXr�a\S-e�YOaqSU_`f/V8a=Y-_���W;Z8Y-[=r�^�moS-_`g S-m ";B WES-a�r�e`_�[=WEe�^�f�mo_`S-g e�h\^r��@a@e�YIÀ�S-m;B��\�\[/e�YqWEZXYO[�r�^�moS-_`g �+^;Z8S-a\TUVba=T�e`S�e�h\^�f/^Q_�V8cIYIe`VbSUanS-m;B � ]�Vbe�h\V8a ��s ���a=WE^{]"^ ]�^{h=Y�cU^�W;S-a=r�e�_`[=WEe�^Qf�e�h=^��\_`SO��^QWEe�V8S-a=r ��v � y]"^�W;Y-aº¯�Vba�r�^Q_�e�±�e`h\^;g�Vba@e`S

e�h=^{_�^�r�SUZb[/e`VbSUan_`^Emo[\e`YIe`VbSUa ' s(��h\^�moS-_`gCYOZ3�\_`S/WE^�f/[\_`^�VXr�f/^;�=a\^Qf��+^;Z8SI]{�� �����������������ºÌ\s ¾����^Ee � ��^�YkWE[\e�j�mo_�^Q^t�\_`S@S-m"S-m � � B>%�� ��� r;s eQs B V8r�cIYOZ8V8f3�

� � � W;ZbS@r�^�fwYOa=f5r�iUS-Z8^;gqVbpQ^QfwY-a=f � e�h\^�S/W;WE[=_�_`^;a=W;^�SOm-B$Vba � s��^Ee ' ÏMYtTU_�SU[\a=f_`^Emo[/e�YIe�V8S-aÅWESU_�_`^Qr��+S-a=f/V8a\TCe`S�Yn_`^Qr�S-Z8[/e�V8S-al_�^;mo[/e`YOe�V8S-a ' S-m�!"��® ��% � ² rQs e�s ' Ï � ' ��s'z^�f/^E�=a=^�YOa �� j��\_`S@S-m ' Ï v �(yV8a=f/[�W�e�V8c-^QZb�1��K^;e�� �+^qYnZ8^QYIm"a\S/f/^�Vba ' Z8Y-��^QZbZ8^Qfl]�V}e`hzY�WEZXYO[�r�^ � �¹moSU_ � �º!"��® ��% � ² Y-a=fkZ8^Ee� � � �" � �.qs��S�� ]�^�YUr�r�V8T-a�e`h\^��\_`SdSOm����k� ��v � y ���@]�h\^;_`^ ��v � y=VXr�e�h\^��\_�S-��^QWEe�V8S-aSOm �#e�S � YUr{f/^E��a\^QflVba¹�^;gqgCY�Ì=sb|qu"�5f/^;�=a\Vbe�V8S-a����­VXr{Y�W;[/e�j�mo_`^;^q�\_`S@S-m�SOm�e�h\^r�^QÐ@[\^;a@e �" %� � ��� �F% �.tsku��ÅY-r`r�[\gq�/e�V8S-a � VXr�W;ZbS@r�^�fzY-a=fÅe`h@[�r����$V8r�YkWE[\e�j�mo_�^Q^�\_`SdSOm�S-m �" %� � � % �.qs��r`r�[\gq^�e�h=YOe�� V8r(Y a=Sdf\^�Vba ' ZXYO�+^;Z8Zb^�f�]�V}e`h � Y-a=f�]�V}e`hC�=YO_`^;a@e�a\S/f/^Qr�� 4"ZXYO�+^;Z8Zb^�f]�Vbe�h � 4�Y-a=f�� N�ZXYO�+^;Z8Z8^Qf�]�V}e`h � NOsM��h\^;aK���d� f/^E�=a=V}e`VbSUa{SOm\Y�_�^�r�SUZb[\e�V8S-a{f/^;_`V8c�YOe�V8S-aK�O!VXr�Y�®�T-_`S-[\a=f�²K_`^Qr�S-Z8c-^QaUeMSOm � 4"Y-a=f � NOs���h\^Q_�^;moS-_`^ � 4 � �" � �. % O� � N�� � % �� � ��YOa�f � � �" % �� � �.G% ��ÃmoS-_�g�[\Zbe�VXr�^Ee`r�SOmKYOe�S-gCr �" % �. % �� % ��¸YOa=fCY-a�YIe`S-g ¸S/W;W;[\_�_`V8a\T��jRe`Vbgq^�r�V8a � 4 Y-a=f *;j�e�V8gq^Qr�V8a � N�K^Ee�� � �"YOa�f�� � ��+^�e`h\^ �� j��\_`SdSOm�r�WES-_`_`^Qr���SUa=f/V8a\T e�S � 4 Y-a=f�� N �@_�^�r��+^QWEe�V8c-^;Z8�-s

��r`r�[\gq^�e`h=YIe�� � �{V8r{Y��\_`SdSOm�S-m �" %� - ��� - % �. % �Y-a=f�� � �SOm � % �� %���� ��� �#% ��moS-_ , % ��� ��s���h\^Qa�� � �/e�h\^ �� j��=_�SdSOm�WESU_�_`^Qr���SUa=f/V8a\T�e`S��¹�/VXr�f/^E��a\^Qf�Y-r

®�� � ��²�" %�� - � � - % �. % �" %�� - ��� - % �. % � � � �

®�� � �² � % �� %��� ��� �C% �� % �� %���� ��� �C% �� � ��� �

�" % �� %� - � � ��� - � �#% �. % �� � ( ��K^;e�� �+^ e�h\^{_`SdSOe�a\S/f/^{SOm ' ÏR¿/e`h\^;a ' ÏRv �(yVXr�f/^;�=a\^Qf�YUr������Os � �m �ÃV8r�Y�WE[\e�j�mo_�^Q^��\_`SdSOmS-m&B %� ��� e�h\^Qa ' Ï�v ��yKVba ��^;�=a\Vbe�V8S-a�Ì\s ¾�VXr�Y��=_�SdSOm�]�V}e`h

YIe`S-gqVXW�WE[\e`r�S-m � % 2�2�2 %� � � %�2�2 2�% � ®�a\SOe`^{e�h=YOe�e`h\^�W;Z8Y-[=r�^���^QZbSUa\T-V8a\TCe`SCe�h\^�_�SdS-ea\S/f/^�SOm ' ÏKVXr � ²Es���a\Z8��YUf\f/Vbe�V8S-a=Y-Z�W;S-a@e�_�Y-WEe�V8S-a=r�Y-_�^�a=^QWE^�r�r`YO_`�tmoSU_�TU^Ee�e`Vba=T�YC�\_`SdSOm�' v ��y(]�V}e`hzYOe�S-gqVXW�W;[/e`r�S-m � ��� Vbe`r�^;Zbm�s� �e{_`^;gCYOV8a=r�S-a\Z8��e�S�^;Z8V8g�V8a=YOe�^�e�h\^CYIe`S-gqVXWWE[\e`rQ¿1e�Ste`h\VXr�Y-Vbg YOad�wWE[\e�j�^;Z8VbgqV8a=YIe`VbSUak�\_`SdW;^Qf/[=_�^�®�^-s T=s�e�h\VXr�V8aºvb|���y«²�f/Sd^Qr�e�h\^���S-�Ks��h\^{Z8^;a\T-e�h�SOm�e�h\^{�\_`SdSOm�r"]�Vbe�hwYIe`S-gqV8W W;[/e`r�VXr�^Qr`r�^Qa@e�VXYOZ8Zb�tf/^;�=a\^�fn�d�Ce`h\^ Zb^Qa\TOe`h�SOm' Ï�s

Page 33: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � ¾U¾

� ������� ���ÉÌ\s8|������;� �°ª���� �;§/� �¬È�¤����K¨+¤`¥Q¥�È"¥�È��{�;�b¥�¦;��Ê�¦;��;§=�;¡=� � �B %� ��� � ��\�;¤��BÉ�X¦"��©��O�¬��Ê�ÈE¥I¤���§/�b�{¥����E§/¤�¤��«¡dË��O� � �«¡ � �I¡1Ê � ��� �X¦�¦ (U¥I�8�E���b£��`Ê����K§/¤��«�=�E¤��C¥I¤`�"�b�E�' Ϫ�����Ë-¤�¥I§/¡1Ê�¤���È�§/���I����¥I¡ ��d�����C��¥I¤�¤��E¦�¨\¥O¡+Ê�¦���¥���¤��E¦E¥O�¬§/����¥I¡t¤��RÈ�§/���I����¥I¡�¥�È(!"��® ��% � ²�I¡1Ê�� ' � �ÉgCYIÀ��� � �76 � �«¡ ' � � �+�=�E¡º�«�=�E¤`�n� U�X¦��R¦���¨1¤�¥Q¥�È �' v �(y�¥�È � � � ��«�«��I��¥I�����q�E§/�R¦��I¡+Ê ��® �' v �(yo² �Ã� &1��® ��² ��® ' ²E®R��� ' � �°|�²(� ��������F��r�^;^Cv ~�y %�SzVbZ8Z8[=r�e`_`YOe�^ne�h\^�]�h\SUZb^��\_`SdW;^Qf/[=_�^�f/^Qr`WE_`Vb�+^QfºYO�+SIc-^t]"^�WES-a@e`Vbad[\^n]�V}e`h»�(À/Y-g�j

�\Z8^�Ì\s8|-s�������������kÌ\s ����K^;e � Ï �+^ e�h\^{�=_�SdSOmMSOmMe�h\^�r�^QÐ@[\^Qa@e

� � =, %�®E���1²E®�"C®$�+² ,/.C®$�1²�² � ®H�) \²E®0"C®�M/²-,/.C®0 /²�²Y-r�f\^E�=a\^�f�Vbaw��À\Y-g��=Zb^{Ì\s8|-s�'z^{h=Y�c-^ r�h\SI]�a�e`h=YIe

!"��® � Ï % � ² � "C®$(3² � .C®$(3²?% � "C®�Md²3% .t®$*/² � �]�h\^Q_�^ � VXr"e�h=^{SdWQWE[\_`_`^;a=W;^�S-m� =, &V8a � s'l^ �=_�r�e�f/^E�=a=^ e�h\^{�\_`SO��^�W�e`VbSUa=r"SOm �"ÏK]{s _Qs eQs�W;Z8Y-[=r�^�r�Vba5!"��® ��Ï�% � ²��'z^�r�e�YO_�e�]�Vbe�h �"ÏRv � 4�y��de�h=^{�\_�S-��^QWEe�V8S-a�SOm �"Ï1e�S � 43��"C®$(3² � .t®$(3²����h\^{�\_`S-�=Zb^Qg$W;Y-an�+^{_�^�f/[=W;^Qfne�S�e�h=^�WES-a�r�e`_�[=WEe�V8S-a�SOm � 4 v � 4 y�+^QW;Y-[=r�^�S-m

!"��® � 4 % � 4 ² � "C®$(3² � .t®$(3² � 2u���f/^E��a\V}e`VbSUa�SOm �-4�Y-a=f�SOme`h\^{�\_`SO��^�W�e�V8S-a� � 4Ov � 4�yVXr�Y��=_�SdSOmMSOm

"C®0(1²3%Q®E�F�+²;®0"C®$�1²-,/.C®0�+²�² � .C®$(3²?2��h\^{ZXY-r�e�Vba/mo^Q_�^Qa=WE^{V8a ��ÏKY-�\�\Z8Vb^�r"e�SCYOa�WE^Qr�e�SU_`r"S-m � Y-a=f�e�hd[=r �"ÏRv � 4 yVXr�f/^;�=a\^Qf�YUr

® �-4Ov � 4�y«²"C®0(1²3%Q®����+²;®0"C®0�+²-,/.t®$�+²�² � .C®$(3²

"C®$(3²?%�®E�F�+²E®�"C®$�1² ,/.C®0�+²�² � ®��) \²E®�"C®0M/²-,/.t®$ \²�²3%O.C®0(1² �·���

'z^{�\_�S/W;^;^Qfº¯�V8a=f/[�W�e�V8c-^QZb�/±qYOa�fnW;S-a=r�e�_`[=W�e � 4 v � 4 y��"C®$(3² � "C®$(3² .C®$(3² � .C®$(3²"C®0(1²3%J"C®0(1² ,/.t®$(3² � .t®$(3² ,°���

"C®0(1²3%Q®E�F�+²;®0"C®$�1²-,/.C®0�+²�² � .C®$(3² �k�5��([\e�e�V8a\Tqe`h\^{�=YO_�e`r"e`S-TU^Ee�h=^;_�]"^�^Qc-^QaUe`[=YOZ8Z8�CS-�/e�YOV8a �"ÏRv � 4�y��

"C®0(1² � "C®$(3² .C®0(1² � .C®$(3²"C®$(3²?%J"C®0(1² , .C®$(3² � .t®$(3² ,°�5�

"C®0(1²3%Q®����+²;®0"C®0�+²-,/.t®$�+²�² � .C®$(3² �w� �"C®$(3²?%�®E�F�+²E®�"C®$�1² ,/.C®0�+²�² � ®��) \²E®�"C®0M/²-,/.t®$ \²�²3%O.C®0(1² �·���

%\SU_ � N � � "C®0M/²"]"^ S-�/e�YOV8ane`h\^{�\_`SO��^�W�e�V8S-a ��Ï�v � N y��"C®0M/² � "C®0M/²

"C®0M/² � "C®0M/²?%L.C®$*/² �·���

� "C®0M/²-,/.t®$*/²?%J"C®�M/² ,¸���

� ®��! /²;®0"C®�Md² ,/.C®$ \²�²?%J"C®�M/² �n���®����+²;®0"C®0�+² , .C®$�1²�² � ®��) \²;®0"C®0M/² ,/.C®$ \²�²?%J"C®�M/² �·���

Page 34: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

¾ � )1*O,/.1)+0123,/4k*-,/687+9;:=< �a�e`h\^�a\^EÀde�r�e`^;��]�^�e`YOiU^�Y�_�^�r�SUZb[\e�V8S-a�_`^Emo[/e�YIe`VbSUa ' SOm1!"��® ��% � ²E�-WESUa=r�e�_`[=W�e�Y�TU_�SU[\a=fV8a=r�e�YOa=W;^ ' ��c@VXY�Y�TU_�SU[\a=f{r�[\�=r�e�Vbe�[/e`VbSUa �CYOa�f Vba=r�^;_�e�Y-�\�\_`S-�\_`V8YOe�^�V8a=r�e`YOa�WE^QrSOm ��v � y �V8aUe`S ' ��s���h\^�_`^Qr�[\Zbe�V8r�YC�\_`SdSOm�]�V}e`h´®oSUa\Zb�\²�YIe�SUgqV8W{W;[/e`r�SOm(Ytr�^QÐ@[\^QaUe � ÏKV8ak]�h\VXW�he�h=^{SdWQWE[\_`_`^;a=W;^ � V8r�^QZbV8gqVba=YOe�^�f3s��^QWQYOZ8Z3e�h=YOe

!"��® � Ï % � ² � � 41�"C®$(3² � .C®$(3²?% � NK� � "C®�Md²3% � Q ��.C®0(1² � ��2%MVb_�r�e�]�^{f/^;�=a\^�Y�_�^�r�SUZb[\e�V8S-a�_�^;mo[/e`YOe�V8S-a���S-m�!"��® ��ÏH% � ²��

� "C®0M/² "C®$(3² � .C®$(3²� .C®�Md² � .C®$*/² �

� �

YOa�f�YqW;S-_`_�^�r��+S-a=f\Vba\T�T-_`S-[=a=ft_`^Emo[/e�YIe`VbSUa ' �� "C®�Md² "C®�M/² � .t®0M/²

� .C®0M/² � .C®�Md² �� �

��h\^{TU_�SU[\a=f�r�[\��r�e`V}e`[/e�V8S-awf/^;�=a\V8a\T�e�h\^{TU_�SU[\a=fn_�^;mo[/e`YOe�V8S-a�V8r� � (54/M�%J* 4 M � 2

�K^Ee��54�� � Ï v � 4`y ��� �&N � � Ï v � N�y �&YOa=f � Q � � Ï v � Q y ��s#%\SU_tYlgqSU_�^wWESUgq�=Y-WEe_`^;�\_`^Qr�^;a@e`YOe�V8S-aÅZ8^Ee�[�r�]�_`V}e`^>B moSU_n®����+²;®0"C®0�+² , .C®0�+²�²�YOa�f � moS-_n®H�) \²E®�"C®0M/² ,.C®0 /²�²�s��h\^;a �' v �"ϬyVXr�SOmMe�h=^ moS-_`g

®�� N ²B � � %O"C®0M/²

®� 4 ²"C®0M/²?%OB � � %O.C®�M/²

B %OB � � % � %O.t®0M/² � ( �®��&Q�²

.C®0M/²?%OB � �B %JB>%JB � � % � % � � ( �

B � � W;S-a@e�_�Y-WEe�V8S-a=r

�' v �"Ϭy�W;YOa��+^�WESUa=r�V8f/^Q_�^�fnYUr�e�h=^{_�^�r�[\Zbe�S-m�Y�e`_`Y-a=r�moSU_�gCYOe�V8S-a�^;Z8VbgqV8a=YIe`Vba\Tqe`h\^�S/W;W;[\_�j_`^;a=W;^�S-m# , V8a � s ��Ï�]�Y-r�f/^;�=a\^QfzY-r ����� �R® ��²�]�h\^;_`^ �#VXr{Yt�\_`SdSOm�S-m B � � s��h\^Q_�^;moS-_`^ �' v �"ÏbyV8r�Y��\_`SdSOmMSOmMe�h\^�r`YOgq^ ^;a=f/j�r�^QÐ@[\^QaUe�]�Vbe�h�S-a=Zb��YOe�SUg�VXW WE[/e�r;s ��S��=[/eKe�h=Vba\T@r3e`S-T-^;e�h\^Q_3]�^�S-�/e�YOV8a Y��=_�S/WE^�f/[\_`^�moS-_KS/WQWE[\_`_�^Qa=WE^;j�^QZbV8gqVba�YIe�V8S-a�;]�h\VXW�h

W;Y-aw��^�e�_�YOa=r�moS-_`gq^QfnVba@e�SnYCWE[/e�j�^QZbV8gqVba=YOe�V8S-a��\_`S/WE^Qf\[\_�^{cdVXY��������Rs"'z^�WQYOZ8Z3e�h\VXr��=_�S-jWE^�f/[\_`^��{!"�����"�w® �(�E§/¤`�E¡1�`� ���"�¬�«���«¡+�O�R��¥O¡zª;¢ ��� �1¥O�¬§/����¥I¡@²"Y-a=fnf\V8r��\ZXY��qe�h\^ gCYOV8ar�e�^;��r���^QZbSI]{��MG�HN �dJ�L�G.� �{!"�������1® �"²���«¡I¨1§/�R���É®�r�i-SUZb^Qg�V8p;^�f=²��=_�SdSOm ���/Y�Z8^Em«e�j�S/W;W;[\_�_`^;a�WE^ � S-m�Y�cIYOZ8VXfqmoS-_`g�[\ZXY�V8ate`h\^�^;a=fdjr�^QÐ@[\^;a@e � SOm ��s¥I§/�}¨+§/�����ÉWE[/e�jRmo_`^;^��\_�SdS-m �ºS-m�e�h\^�^;a=f/j�r�^QÐ@[\^QaUe � ]�Vbe�h\SU[/e�e`h\^�moS-_`g�[\ZXYCS/W;W;[\_�_`V8a\TYIe � �|-s�!�S-gq�\[\e�^�!"��® ��% � ²�s�/s�!�S-gq�\[\e�^{Y�T-_`S-[\a=fn_`^Qr�S-Z8[/e�V8S-a�_�^;mo[/e`YOe�V8S-a ' SOm�!"��® ��% � ²�s¾\s�!�S-gq�\[\e�^ k� �' v �(y�s�=s��(Z8V8g�V8a=YOe�^�e�h\^�YOe�SUg�VXW WE[/e�r�V8a �s

Page 35: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

4+,\9��3*��+7�6��30l7�<1,��34�,����/4��36X0 � ¾@~

��h\^Qane`h\^�WE[\e�j�^;Z8VbgqV8a=YIe`VbSUa��=_�S/WE^�f/[\_`^�Vbe`r�^;Zbm�V8r�r�V8g��=Zb��f/^E�=a=^Qf�Y-r

!"�������1® �"² �°�{!"�������1® � � ��� ® �"²�²32���;�C�I¤)(�����r�e`h\^�]"S-_�r�e�j�WQY-r�^�W;S-gq�\Z8^EÀ/V}e��nSOm(WE[\e�j�^;Z8VbgqV8a=YIe`VbSUa�VXr�a=S-a\^QZb^Qg�^Qa@e`YO_`�5®�VRs ^-sVbe`r e`Vbgq^tWESUgq�\Zb^;À/V}e��zW;YOa=a\SOe{�+^C��SU[\a=f/^�fl�d�5Y��=Àd^�f5Vbe�^Q_`YOe�V8S-azSOm"e�h\^C^;À/��SUa\^;a@e�VXYOZmo[\a=WEe�V8S-a�²�]"^�WQYOa\a\S-e�^;Àd�+^QWEe�!"��������e`S��+^�r�V8g��=Zb�tY�m�Y-r�e"YOZ8T-SU_�Vbe�h=g�s���SI]"^;cU^;_�V}e�V8rr�h\SI]�anV8aÅv ~Iy+e`h=YIe��/moS-_�r�S-gq^ r�^�ÐU[=^;a=W;^Qr�SOm �� j��\_�SdS-m�r;��!"�������tT-V8c-^Qr�Y�a\S-a=^;Z8^;gq^;a/je`Y-_��{r���^Q^Qfdj�[\��SOm���^;a@e`p;^;a r��\_`SdW;^Qf/[=_�^Us���h\VXr�r��+^;^Qf/j�[\��V8r��=YUr�^�f{S-a�Y�¯�_`^Qf/[=a=f\YOa�WE�/±YIe�e�h\^tYOe�S-gqVXWqZb^Qc-^QZ(SOm"e�h\^C�=_�SdSOm�r�]�h\V8W�h¹WQYOaÅ��^tf\^Ee�^�W�e`^QfÅV8aÅe�h\^tW;S-a=r�e�_`[=W�e`VbSUaÅSOme�h=^ r�^Ee�SOm�WEZXYO[=r�^Qr�!"��® ��% � ²E�/�\[/e�a\SOe��d����^;a@e`p;^;a r"�\_`S/WE^Qf\[\_�^UsMu"�qe`h\^{Y�c�Y-VbZXYO�=VbZ8V}e��SOm3^;ÁCW;Vb^Qa@e(_�^;�=a\^;gq^QaUe�r�Y-a=fqr�^�YO_�W�h�r�e�_�YIe`^;T-V8^QrMmoSU_(_`^Qr�S-Z8[/e�V8S-at!"�����"��YOZXr�S �+^;_�moS-_`gqrÐ@[\Vbe�^{]"^;Z8ZKVba�^EÀ/�+^;_`Vbgq^QaUe�r�®�r�^;^Cv ÌIyo²�s �

4+,��U,/4+,/03:\,\9� Ñ��������� ������������������� �"!$#&%'�)(*!'+ �,.-/- �10&!123�4%'576��48�%/9:9��4!<; �0>= - 0 , 9:#3! �,.? 2&� �[email protected]�G"HIB.DFJLK>M"E�GONQP�R

PB�STG"P��VU3W&XFYUÑ4Z&Z\[RÑ4]&^&_3`:��aVabY�c&d&_"e�cgf3].Y� ^>��h*�Ai7����j����lkgmVn��o�qp.�sr�j������ ��ts% u ? 035v%vw&tl5'=.�:w&!�x �Ay\B�P�zV{}|&|�~l|}��B���D |3H�B.D�G}z��}G4B�K>|�P�JFP��

['�)Y��*W&�V��mV� W&mOkgmVn��)Y.��W&�1W&m.�&W"U��s�}nV� �1W&� ��`:�VU3W&XFYV�:�V�qX��1��U����}�����4���}mV�}�&��^&Z&Z�Ñ&�saVa�YVf&f3�"e��&d&^.Y� d>�����i7�����������bh�����)��� >  ������kgmVn�<��¡���¢�£V¤��.¥���¦ t�w&ts§ � - �4¨$�"ts5F03!�x©9Fª��:�:#&§ , ª«%'t©ª�!�w"w + - �4t�635'=

�4x¬915F! ,V? 5 , !�0 -?"- 0 , 9��*+�w&!�¨­5F!�0&ts9/+}w&!�¨<035v%vw&t ��®��4|&M3¯°S J�MgK4�@Ñ4]&]gfV�VaVabY�^�Ñ4d"e�^�Ñ4].Y� fg����Ai7�����\kgmVnl<��¡���¢�£s¤���¥�²± , 5Qt�w&!�¨<0 - +�w&!�¨<9©0&t�#�ª�!�w4w1+ ? w&¨�ª - �:³3%/5Fx �qNQPbP�B.S�K«|��O®����4G

B�P�z�N�´V´�S J�G}z\µ|}��J�Mg�.U3W&XFY�]3¶·[�Ñ4]&]&]3`���aVa�Y@Ñ4^3¶4eOÑ"¶&¶�Y� �>� �A± , 5F§�� - %/¨<%/t�0&5F%'w3t\0&t�#$! �1# , t�#303t ? x&§�� - %/¨<%/t�0&5F%'w3t��}x<!��"9:w - , 5F%'w&t ��¸�¯�¹�º�HI{}|.S J�MO»*|�HOR

´���D�B.DFJ�|�P��.U3W&XFY�^&]�[v^&Z&Z&Z3`:��aVabYdÑ}f3]"eOÑ"¶gc.Y� c>�����i7�������b<��¡���¢�£s¤��.¥��kgmVn«¼$����½�¤:������¾ x&9:5¿�4¨À#3�"9 ? !�% ª�5F%'w&t�Á ± , 5v! �49ÃÂ&ÄgÅ ?", 5*� - %/¨<%/t�0&5F%vw&t

�4x«! �49�w - , 5F%vw&t �¬»*|�P��3G"�}G"PM}GÆ|�PÇB3�bD�|�HIB.D�G}zÈz.G4z3��MgDFJ�|3P�ÉOM}BVz.GgR�ÊsË��°Ì��}��� ÍV�1��ΰWg�1�}�©��ml��� � � Ïs�}�TkgX�¿m3�1�}X�X���Ð&�}mV�}�&����aV�1��m.Ð&�4�4�@Ñ4]&]&].��aVa�Ys^�Ñ4^"e�^�Ñ4c.Y

� ¶"������i7���s����r�¤OkgmVnÈ����pV�.¥ �½���Ñ3¢��� ��   � ; , ¨Ò�4ts5F9 ? =.�4%v# , t�6&9Fª�!�w�� - �4¨Ó#3�"!I¨$0&5'=.�4¨$0&5F%/9 ? =.�"t- w163%�2 ��@ÔB�D¿E�G"H�B.DFJLK"M"E�G·NQP�PB.STG"P��VU3W&XFYs]&]\[�Ñ4]&^&_3`���a.abYsdgf3^"e�d3¶g^.Y

� _>�A¼$��i*½�½   ����NQPlJFPbÕ�GgK4DFJ'�VB.DFJ�|�PÆ|�PÖDFE�G©STB�×�K©|}��DFE�|��V��E�DL�sØ�W4U3�}��Ù�ÍV�VX����4k>�1��W&m.�"�dÑ4]&�&_.Y� ]>��Ú���i �½��VÛ�������Ú��7¼Q� ���j��   �7kgmVnlÜ$��¼ � �s�3Ý�¢T��¥�QÞE�GÆ»7STB.K4K�J�M}B.S�ß·G}M"JLK�J�|�Pà®��}|V{gSTG"HI��Ù�4��á

�1a��}���1� U3�}����mOâIk>� ãV�}ä©k>�1���4kgXbÌbW&Ð&���3����aV�1��m.Ð&�4�4�@Ñ4]&]3¶�Y� Ñ4Z>��)����¥ � �s�.¥��¦ t�w&5¿�\w&t�5'=.�·�"ts5F9 ? =.�"%'# , t�639Fª�!�w�� - �"¨ �QÞE�G�¸b|����"PB.S�|}��¹�º�HI{}|.S J�MIµ�|}��J�Mg�

U3W&XFYdÑ$[�Ñ4]&d&c3`:��aVabYVf3Z"e�f&fVY� Ñ�Ñ���O���3£V¢���å��gÝ�¢T¤QkgmVnOæ�¢   ���&r�ç � £V�������s¦è± w&¨�ª , 5v%'t�6$é7!�w ? �1# , !��°+}w&!©ê , 0&ts5F% u ? 0&5F%'w3tìëb=.�"§

w&!�x ��¸b|����>P�B.S�|}�©D¿E�G©N·»�@Æ�VU3W&XFY�¶©[RÑ4]&c&Z3`:��mVWVYsd.�VaVabYs^&Z�Ñ:e�^�Ñ4�.Y� Ñ4^>��Ú��bÚqj�������íÃGgSTB�D¿JvÕ�G\M}|�H¬´bSTG"î�JLDFJ�GgK©|���ï*�&K4DLR:|��4z.G"�IM}B.STM"��S JL��������ð7�}ÐV�dÑ4]&]&^.Y� Ñ4d>��ñ)��Ú�Û   r�kgmVnóò²��ô���£V¥��7õ t�5'=.��ª�! 0 ? 5F% ? 0 -Aö 0 - , �¬w +<#&% ÷��4!��"ts5°#3�¿u�ts%/5F%vw&t�0 - 5F!�0&ts9 - 0&5F%'w&ts9)5¿w

t�w&!�¨$0 - +�w&!�¨ ��®��4|&M3¯Q|}��M}BVzVGgR�Ê�ø.��Ì��}��� ÍV�1�©Î°Wg�1�}�Q��m������1� Ïs�}�TkgX�¿m3�1�}X�X���Ð&�}mV�}�&��U3W&XFY�Ñ�Ñ4ZgfV����aV� ��mVÐ&�}�"�Ñ4]&]&c.��aVabY.f3Z&d"e�f�Ñ"¶�Y

� Ñ}fg�A����h����� ��� >  �����q<��¡���¢�£s¤���¥A�*ò²��ò���7����£��7kgmVnlù)�7ú����7½VÝ��íÃGgK"|.S ��DFJ�|�PÈH�GgDFE�|&z.K<�&|��DFE�G\z.G4M"J¿K}J�|3P�´��}|V{gSTG"HI�sÌb�4��� ÍV�1�ÃΰWg�1�}�°��m���� � � Ïs�}�TkgXb�¿m3�1�}X�X���Ð&�}mV�}�&�sU3W&XFY�c3¶g].����aV� ��mVÐ&�}�"�UÑ4]&]&d.Y

� Ñ4�>�A¼$��h�s��Û����7û �¿63!�% ÷°9:9 ? =.!�% +:5'Å)�"%/t��I#3�"!�03!�%/5'=�¨$�45F%/9 ? =.�"tìt�0 ? =&6��>�4% - #3�"5F�·ü7w&!�¨<� - 9vª�!�0 ? =.��#3�"9!��"%/t��"t«ýÃ�4t.23�4ts9 �þ��4|�HÓþ��}G �VGóD |Cÿ��|VzVGgS � N K"|����4M}G&{}|&|�~lJFPCHIB.DFE�G"H�B.DFJ�M}B.S°ST|}��J�MóÊ�������Ê��.øsÊ[ �sY.U&kgm��°�4� ���}mVW�W&� �4�V�}nV� � W&��`:����kg��U&kg�1n���mV� U3�}� �1� ���©Ùq� �}�1�"�UÑ4]&c3¶�Y

� Ñ4c>��æ)��¼Q�   ���s��£.������� �:0 - %��"0&5F%'w&tlw +¬0·63�:w&¨$�45F!�xO5'=.�:w&!��"¨ ª�! w ö %'t�6I¨$0 ? =�%/t�� �®��4|&M}G}G}z�JFP��.K�|}�DFE�G©JvP�D�G"�>P�B.DFJ�|�PB�S�M}|�P��&G"�4G"P�M4GI|3PìJvP��&|��>HIB.DFJ�|�P�´��4|&M}GgK4K}JvP��.���&ÍVmV��Ñ4]&�&].�saVa�Y�^3¶gd"e�^&_&^.Y

� Ñ"¶"�A¼$� ¼Q����£s�"����� �ts5F�"!�9 ,.? = , t�63�"t �, �1�4! #30&9 - w:6&%'9 ? =.� 9 ? = - %'���A�4t � @CB.DFE�G"H�B�D¿J¿K>M"E�G� G"JLDLK>M"EV�"J �gD���U3W&XFYsd&]\[�Ñ4]&dgf�`���a.abYVf3Z&�"e�f3d�Ñ&Y

� Ñ4_>��ç�� ���¼�¢   �7½��s���s¦ ª�!�w"w +)¨$�45'=.w"#�+}w&!�� , 03ts5v% u ? 0&5F%'w&t�5'=.�:w&!�x�ÁQ%/5F9�� , 9:5v% u ? 0&5F%'w&t�03t�#·!��:0 - % �"0&§5F%'w&t ���! �@ ¸�¯AíÃGgK>¯qß©G"Õ.¯'�b[�Ñ4]&c&Z3`���a.abY�^&_"e�d&�.Y

Page 36: Home | Theory and Logic · Î{Ï"WES-ar VXr e`Vba=TwSOm Vbar e YOa=W;^Qr S-m e h\^tgCYOe _`V}ÀÅ] h\VXW h¹V8r [\a=r`YIe VXr YO \Z8^Ce`S@Ssw h\V8r T-V8c-^ r Y¹r Vbgq \Z8^w_ ^ f/[=WEe

¾-Ì )1*O,/.1)+0123,/4k*-,/687+9;:=<� Ñ4]>��Ü<��¼Q¢��s���sj��&®��4|&|}�QDFE�G}|��>º·B3Pz$ST|}��J�M}B.S�M}|�H¬´bSTG"î�JLDFº.�3��� ÍVnV���}����mQÙ��1W�W����*ãV�}W&� �3�������.X���W&a�W&X����4�

Ñ4]&_3¶�Y� ^&Z>���¬��¼ �½�j��   � �, �1�4!Ã+�w3!�¨<0 -�, t��4ts5F9 ? =V�4%v#��10&!�� ¾ �0&5 �4�«#3�"!·é7!�%'t ? % ª�%'0��0&5'=.�"¨$0&5F% ? 0 , t�# ö �"!�§

8�03t�#&5¿�4! ¾ x&915¿�"¨<� �V@Ô|3PB.DLK�E�G��&D�G²������[email protected]�G"H�B.DFJF~���Pz\®�EVº.K�JF~��sU3W&XFYsd&_�[�Ñ4]&d�Ñ"`:��aVabYdÑ"¶g�"eOÑ4]&_.Y� ^�Ñ�� � (7%'t ¾ ª.� �4%v0 - +}0 -/- #3�"9�(*ts5F9 ? =.�"%'# , t�639Fª�!�w�� - �"¨<9*#3�4!q5'=.�:w&!��"5F%/9 ? =V�4t��w163%�2 ���*� �VG&{"PbJLK4K"G

@CB.DFE�G"H�B�D¿J¿K>M"E�G"�� �|.SvST|��"��JLG"P��sU3W&XFYs^·[RÑ4]&d&^3`:��aVabYV^3¶4e�^&_.Y� ^&^>��ôÃ�<æ ���¥��   ��� ë�0�� - �:0 , ³à0&t�#È!�� - 0&5¿�:#Ô¨$�45'=.w"#&9 �·y\B3PzV{}|&|�~ |��ÔNQ��D |3H�B.D�G}z í²G4B�K>|�P�JFP��

['�)Y��*W&�V��mV� W&mOkgmVn��)Y.��W&�1W&m.�&W"U��s�}nV� �1W&� ��`:�VU3W&XFY@Ñ&�V�qX��1��U����}�"�.^&Z&Z�Ñ&��aVabY@Ñ4Z�Ñ:eOÑ"¶g_.Y� ^&d>�����qæ������V�s����j���¾ , ! - �<ª�!�w�� - ����4¨$�<+}w&t�#30&¨$�"ts5F0 - #3� - 0 - w163% � , �O¨$0&5'=���4¨$0&5F% � , � ��¹�´��4B�×�|��&R

zVB�P�J�B�·´�|.K�J�G}z���G"PÇÞ�|�×�B����>ºVK4D�B��\B���~�|�×�G��V|��lB��gK��3B�×�K}~&JLG �V|�É �«ºVz��>J�B.S � �!�>�bU3W&XFY�^gfó[�Ñ4]&d�Ñ"`��aVabY@Ñ4^"e��&c.Y

� ^gfg��å$��æ�¢   �V���3£ÔkgmVnà�o��°�. �������������©ÿ��"��Pz�� ��s�VGàzVG"�ÆDFE�G}|��4GgDFJLK"M"E�G"Pǵ�|}��JF~��Q��aV� ��mVÐ&�}�"����}�1X���mb�UÑ4]&^&_.Y

� ^&�>��å$��æ�¢   �.���3£Okgm.n�ç��bi7���s����r�¤>�Aÿ��>��Pz�STB&�VG"Pàz.G"�©@CB.DFE�G"HIB.DFJF~�����a.�1��mVÐ&�}�"�UÑ4]3¶gZ.Y� ^&c>�����!��½Vr��������3¦ , 5¿w&¨$0&5¿�:#$5/=V�1w3!��4¨�ª�!�w ö %/t�6¬0&t�#<5/=V�Q#3� ? %'91%vw&t$ª�!�w�� - �4¨ �.®�E�¯�ß�¯DFE�GgK}J¿K"����kg��á

U&kg� n �°mV� U3�}�1�1� ���3�UÑ4]3¶gd.Y� ^3¶"����� æ<����½Vr�������� � �"9�w - , 5F%'w&tÔ9:5F!�0&5¿�L63%'�"9�0&9I#3� ? %/9:%'w&t�ª�! w ? �:# , ! �49 �Q¸�|3���"PB.S)|}��D¿E�G�N·»�@Æ�

U3W&XFY�^&d�[�Ñ4]3¶gc3`:��aVabYsd&]&_"e�f�Ñ"¶�Y� ^&_>��ôÃ����½�"7�   ¤: �¢�kgm.n«ç��bæ��3r���¤>�b¾ �"¨<0&ts5F% ? 5v! �1�"9²%'tó0 , 5¿w&¨<035v% ? 5'=.�:w&!��"¨ ª�!�w ö %'t�6 �b@ÔB.M"EVJFPG

JFP�D GgSvS J'�VG"PM}G²[#��Y.âO�}X �%$}�}�*kgmVn·Ø)Y�âO���:ãV���&���4n.� �1W&� ��`:��U3W&XFYV¶�����ä¬�}�1���4kgm¬�qX�� ��U.���}�"�OÑ4]&c&].�.aVabY._3¶4eOÑ4Z�Ñ&Y� ^&]>�A¼$�����²¡���¢&�V��¢T�3�I± 0 - ?",.- , 9ó! 0&5F%'w ? %/t�035Fw3! �©¹ �B�HIDLS J�M"E�GÔK"M"EV�>J �&D�G"P­��Pz {"�"J�G��&Gì['Ùq� �4Í.�1�1����á

�:ãV�²���gkgnV�}ä¬����nV�}�('Æ��� �1�}mV� �:ãsk)�/�1�}mb���}nV� � W&��`:���*�4���1ãV�}XF�sØ�kg� ä¬� �1kgn.�"�UÑ4]&^&d.Y� d&Z>��)��¡���¢�£s¤��.¥��²ÞAE�GI�4GgK"|.S ��DFJ�|�PoM}B.STM"��S ��K"�q��aV� ��mVÐ&�}�"Y*����+�� �<��m �*ãV�}W&�1���1���4kgX(,�W&ä¬aVÍ��1�}�)���}� á

�}mV�}�&�/Ñ4]&]3¶�Y� d�Ñ�����½�¥����o��¡   ½Vr�j���þ�|���PzVB.DFJ�|3P�K·|}�·ST|}��J�Mô��4|}���4B3H\H\JvP��.���1�}�}W&mVnO�}nbY��s��aV� ��mVÐ&�}�"�@Ñ4]&_3¶�Y� d&^>��¡��¡ �½�"²����¥���¢T��� ��A�1�"!-� �w"6 - % ? =�2&�"%/5¿�"t�%/¨ � � - 0&5F% ö 230 - 2 �,.- ��@CB.DFE�G"HIB.DFJLK>M"E�GINQP�PB.STG"P��bU3W&XFY

c&_\[�Ñ4]�Ñ4�3`���aVa�Y@Ñ4c&]"e�^&Z3¶�Y� d&d>��)��O���3£V�  g  ¢qkgmVnóñ<��I½���£&�������s¢F� �ts% u ? 0&5F%vw&t�%/t - %'t��103!<5F%'¨<�¬0&t�#O9Fª.0 ? �>Á¬0O9:5F! ,V? 5 , !��:#

ª�!��"9��4ts5¿0&5F%vw&t ��Þ�G}M"EVPbJLM4B�SAíÃG:´�|��gD �.Ë�R:ÊsË��s�¿���1� � Í.� W¬nV�b�}XTkg��W&�:k�$}��W&mV�²nV�}X�XTk<��m.�vW&� ä©k�$4��W&m.�3�-Ñ4]3¶gc.Y� dgfg�Apb� Ü$�.�O��¤   ½sÝ� ë�=.��%/t ö �4!�9���¨<�"5'=.w4#7+�w3!��"915¿0�� - %/9 =�%/t�6)#3�:# ,V? %v�4% - %/5Fxq+�w3! - w:6&% ? 0 -�? 0 - ?",.- % �.®��4|&M3¯

¹bD�G"~�ST|�Õ �"P�K"D ¯[email protected]�¯'��U3W&XFY�]&_�[�Ñ4]&c&_3`���aVa�Ys^&�"e�]&c.Y� d&�>�����7�I��� � �����q¾ w - , 5F%vw&tÖw +©5'=.� � w��>�4%/ts9²ª�! w�� - �"¨ ��¸�|3���"PB.S�|}��NQ��D |3H�B.D�G}z�í²G4B�K>|�P�JFP��.�

U3W&XFYdÑ4]�[�Ñ4]&]3¶&`:��mVWVY�d.�Va.abY�^&c&d"e�^3¶gc.Y� d&c>�����.)�.ô*½!�V¢���¤�½�����¦ , 5¿w&¨<035v% ? #3�:# ,V? 5F%vw&t·8�%/5'=)=.x�ª��"!�!��49�w - , 5v%vw&t ���"P�D�G"�>PA¯�¸b|����>PB�S�|}��»*|�HOR

´���D�G"�·@CB.DFE�¯/�.U3W&XFY@Ñ<[RÑ4]&c&�3`:��aVabY�^&^3¶4e�^&dgfVY� d3¶"� ��¦ ¨$0 ? =�%/t��"§�w&!�%v�4ts5¿�:# - w:6&% ? �10&9��1#Iw3t�5'=.�$!��"9�w - , 5F%'w&t\ª�!�%'t ? % ª - � ��¸�¯7N<K"K"|&M3¯)»*|�HOR

´���D ¯q@CBVM"E�¯'�.U3W&XFYdÑ4^·[RÑ4]&c&�3`:��aVabY�^&d"e�f�Ñ&Y� d&_>�A¼$��ò��� �� � £.¢F��®��}|&|}��DFE�G}|��>º.�s�1�}�}W&mVnO�}nbY��sÎ�W&� � ã.á �°W&X�XTkgmVnb�UÑ4]&_3¶�Y� d&]>��)�sò � �s¢���ÛA�õ t ? w&¨�ª , 5¿0�� - �)t , ¨¬�1�4!�9�8A%'5/=�03tO0}ª3ª - % ? 0&5F%'w&tI5¿w<5'=.��(*ts5F9 ? =.�"%'# , t�639Fª�!�w�� - �"¨ �

®��4|&M3¯�|}�©D¿E�G¬µ�|�PzV|3Pì@CB.DFE�¯7¹�|&M3¯'��U3W&XFY����}�4Y�^·[�Ñ4]&d&c�/gd3¶&`���mVWVYVf3^.�saVabYV^&d&Z"e�^&c&�.Y

)+*-,/.+)10123,/4C*O,/6X7�9Q:\<107��32 36X,/0+01)10

�E) F�34�6X7�,/019;7=4+)39;9E,452 4J4 04 4 � 4 368,/0101)10�)�39;7=4+68)(7§L¨$0&% -76 X��}� �1� �:ã!8�X�W&Ð&���&Y k>�