Модальная версия II теоремы Гёделя о неполноте и система Маккинси.
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03.10.2002
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Abstract
We are going to discuss certain systems (K4.G and K4.Grz) of modal logic that are of special interest in connection with the study of the notions of provability in Peano Arithmetic. K4.G (respectively, K4.Grz) is the result of adjoint a modal version G of the second incompleteness theorem (respectively, the formula Grz) to the modal system K4.
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Esakia L. Модальная версия II теоремы Гёделя о неполноте и система Маккинси. // Logicheskie Issledovaniya / Logical Investigations. 2002. VOL. 9. C. 292-300.
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References
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ЭсакиаЛ. К теории модальных и суперинтуиционисткюс систем //Логический вывод. М.: Наука, 1979.
Эсакиа Л . Слабая транзитивность - реституция // Логические исследования. Вып. 8. М.: Наука, 2001. С. 244-255.
Boolos G. The Logic of Provability. Cambridge: Cambridge University Press, 1993.
Grzegorczyk A. Some relations systems and the associated topological spaces // Fund.Math. 1967. Vol 60. P. 223-231.
Godel K. Eine Interpretation intuitionishen Aussagenkalkulus // Ergebnisse eines mathematischen Kolloqiums. 1933. Bd. S. 39-40.
McKinsey J.C. On the syntactical construction of systems of Modal logic // Journal of Symbolic Logic. 1945. Vol. P. 83-94.
Prior A. Past, Present and Future. Oxford: Clarendon Press, 1967.
Segerberg K. Decidability of S4.1 /7 Theoria. 1968. Vol. 34. P. 1-15.
Smorinski C. Self-Reference and Modal Logic. Berlin: Springer-Verlag, 1985.
Smullyan R. Forever Undecided. Oxford: Oxford University Press, 1988. lO.Solovay R.M. Provability interpretations of modal logic 11 Israel Journal of Mathematics. 1976. Vol. 25. P. 287-304.
ЭсакиаЛ. К теории модальных и суперинтуиционисткюс систем //Логический вывод. М.: Наука, 1979.
Эсакиа Л . Слабая транзитивность - реституция // Логические исследования. Вып. 8. М.: Наука, 2001. С. 244-255.