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NOTES ON BOUNDED INDUCTION FOR THE COMPOSITIONAL TRUTH PREDICATE

Published online by Cambridge University Press:  30 March 2017

BARTOSZ WCISŁO  and
MATEUSZ ŁEŁYK
BARTOSZ WCISŁO*
Affiliation:
Institute of Philosophy, University of Warsaw
MATEUSZ ŁEŁYK*
Affiliation:
Institute of Philosophy, University of Warsaw
*
*INSTITUTE OF PHILOSOPHY UNIVERSITY OF WARSAW WARSAW, POLAND E-mail: [email protected]
†INSTITUTE OF PHILOSOPHY UNIVERSITY OF WARSAW WARSAW, POLAND E-mail: [email protected]
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Abstract

We prove that the theory of the extensional compositional truth predicate for the language of arithmetic with Δ0-induction scheme for the truth predicate and the full arithmetical induction scheme is not conservative over Peano Arithmetic. In addition, we show that a slightly modified theory of truth actually proves the global reflection principle over the base theory.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 3 , September 2017 , pp. 455 - 480
Copyright
Copyright © Association for Symbolic Logic 2017 

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References

BIBLIOGRAPHY

Cieśliński, C. (2010). Truth, conservativeness and provability. Mind, 119, 409–422.CrossRefGoogle Scholar
Enayat, A. & Visser, A. (2013). New constructions of satisfaction classes. Logic Group Preprint Series, 303, 1–15.Google Scholar
Fujimoto, K. (2010). Relative truth definability in axiomatic truth theories. Bulletin of Symbolic Logic, 16, 305–344.Google Scholar
Hájek, P. & Pudlák, P. (1998). Metamathematics of First-Order Arithmetic. Berlin: Springer-Verlag.Google Scholar
Halbach, V. (2011). Axiomatic Theories of Truth. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Horsten, L. (1995). The semantical paradoxes, the neutrality of truth and the neutrality of minimalist. In Cortois, P., editor. The Many Problems of Realism. Studies in the General Philosophy of Science. Tilburg: Tilburg University Press, pp. 173–187.Google Scholar
Kaye, R. (1991). Models of Peano Arithmetic. Oxford: Oxford University Press.Google Scholar
Ketland, J. (1999). Deflationism and Tarski’s paradise. Mind, 108, 69–94.Google Scholar
Kossak, R. & Schmerl, J. (2006). The Structure of Models of Peano Arithmetic. Oxford: Clarendon Press.Google Scholar
Kotlarski, H. (1986). Bounded induction and satisfaction classes. Zeitschrift für matematische Logik und Grundlagen der Mathematik, 32, 531–544.Google Scholar
Kotlarski, H., Krajewski, S., & Lachlan, A. (1981). Construction of satisfaction classes for nonstandard models. Canadian Mathematical Bulletin, 24, 283–293.Google Scholar
Leigh, G. (2015). Conservativity for theories of compositional truth via cut elimination. The Journal of Symbolic Logic, 80, 845–865.Google Scholar
Shapiro, S. (1998). Proof and truth: Through thick and thin. Jornal of Philosophy, 95, 493–521.Google Scholar