A case for satisfaction classes: model theoretic vs axiomatic approaches to the notion of truth
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09.04.2013
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Abstract
One of the basic question we can ask about truth in a formal setting is what, if anything, we gain when we have a truth predicate at disposal. For example, does the expressive power of a language change or does the proof strength of a theory increase?
Satisfaction classes are often described as complicated model theoretic constructions unable to give useful information toward the notion of truth from a general point of view. Their import is narrowed to a dimension of pure technical utility and curiosity. Here I offer an application of satisfaction classes in order to show that they can have a relevant role in confronting proof theoretical equivalent theories of truth.
Satisfaction classes are often described as complicated model theoretic constructions unable to give useful information toward the notion of truth from a general point of view. Their import is narrowed to a dimension of pure technical utility and curiosity. Here I offer an application of satisfaction classes in order to show that they can have a relevant role in confronting proof theoretical equivalent theories of truth.
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How to Cite
Strollo A. A case for satisfaction classes: model theoretic vs axiomatic approaches to the notion of truth // Logicheskie Issledovaniya / Logical Investigations. 2013. VOL. 19. C. 246-259.
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References
Boolos, G.S., Burgess, J. P., and R. C. Jeffrey, Computability and Logic, Cambridge University Press, 2007.
Engstrom, F., Satisfaction Classes in Nonstandard Models of Firstorder Arithmetic, Thesis for the Degree of Licentiate of Philosophy Department of Mathematics Chalmers University of Technology and Goteborg University, 2002.
Friedman, H. and Sheard, M., An Axiomatic Approach to SelfReferential Truth, Annals of Pure and Applied Logic 33:1–21, 1987.
Halbach, V., Axiomatic Theories of Truth, Cambridge University Press, 2010.
Kaufmann, M., A Rather Classless Model, Proceedings of the American Mathematical Society 62(2):330–333, 1977.
Kaye, R., Models of Peano Arithmetic, Oxford Logic Guides, Oxford University Press, 1991.
Ketland, J., Deflationism and Tarski’s paradise, Mind 108(429):69–94, 1999.
Kossak, R., A Note on Satisfaction classes, Notre Dame Journal of Formhal Logic 26(1):1–8, 1985.
Kotlarski, H., Full Satisfaction Classes: A Survey, Notre Dame Journal of Formal Logic 32(4):573–579, 1991.
Kotlarski, H., Krajewski, S. and Lachlan, A. Construction of Satisfaction Classes for Nonstandard Models, Canadian Mathematical Bulletin 24:283–93, 1981.
Krajewski, S., Nonstandard satisfaction classes, Springer Lecture Notes in Mathematics, 537, 1976.
Lachlan, A. Full Satisfaction Classes and Recursive Saturation, Canadian Mathematical Bulletin 24:295–297, 1981.
Robinson, A., On languages which are based on non-standard arithmetic, Nagoya Mathematical Journal 22:83–117, 1963.
Shapiro, S., Proof and Truth: Through Thick and Thin, Journal of Philosophy 95:493–521, 1998.
Sheard, M., A Guide to the Truth Predicate in the Modern Era, Journal of Symbolic Logic 59(3)1032–1054, 1994.
Tarski, A., The Concept of Truth in Formalized Languages, in A. Tarski (ed.), Logic, Semantics, Metamathematics, Oxford: Oxford University Press, 1956, pp. 152–278.
Engstrom, F., Satisfaction Classes in Nonstandard Models of Firstorder Arithmetic, Thesis for the Degree of Licentiate of Philosophy Department of Mathematics Chalmers University of Technology and Goteborg University, 2002.
Friedman, H. and Sheard, M., An Axiomatic Approach to SelfReferential Truth, Annals of Pure and Applied Logic 33:1–21, 1987.
Halbach, V., Axiomatic Theories of Truth, Cambridge University Press, 2010.
Kaufmann, M., A Rather Classless Model, Proceedings of the American Mathematical Society 62(2):330–333, 1977.
Kaye, R., Models of Peano Arithmetic, Oxford Logic Guides, Oxford University Press, 1991.
Ketland, J., Deflationism and Tarski’s paradise, Mind 108(429):69–94, 1999.
Kossak, R., A Note on Satisfaction classes, Notre Dame Journal of Formhal Logic 26(1):1–8, 1985.
Kotlarski, H., Full Satisfaction Classes: A Survey, Notre Dame Journal of Formal Logic 32(4):573–579, 1991.
Kotlarski, H., Krajewski, S. and Lachlan, A. Construction of Satisfaction Classes for Nonstandard Models, Canadian Mathematical Bulletin 24:283–93, 1981.
Krajewski, S., Nonstandard satisfaction classes, Springer Lecture Notes in Mathematics, 537, 1976.
Lachlan, A. Full Satisfaction Classes and Recursive Saturation, Canadian Mathematical Bulletin 24:295–297, 1981.
Robinson, A., On languages which are based on non-standard arithmetic, Nagoya Mathematical Journal 22:83–117, 1963.
Shapiro, S., Proof and Truth: Through Thick and Thin, Journal of Philosophy 95:493–521, 1998.
Sheard, M., A Guide to the Truth Predicate in the Modern Era, Journal of Symbolic Logic 59(3)1032–1054, 1994.
Tarski, A., The Concept of Truth in Formalized Languages, in A. Tarski (ed.), Logic, Semantics, Metamathematics, Oxford: Oxford University Press, 1956, pp. 152–278.