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Relative Truth Definability of Axiomatic Truth Theories

Published online by Cambridge University Press:  15 January 2014

Kentaro Fujimoto
Kentaro Fujimoto*
Affiliation:
Merton College, Oxford OX1 4JD, UK, E-mail: [email protected]
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Abstract

The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overviewof recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 16 , Issue 3 , September 2010 , pp. 305 - 344
Copyright
Copyright © Association for Symbolic Logic 2010

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References

REFERENCES

[1] Beklemishev, L. D., Proof-theoretic analysis by iterated reflection, Archive for Mathematical Logic, vol. 42 (2003), pp. 515–552.Google Scholar
[2] Cantini, A., Notes on formal theories of truth, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 35 (1989), pp. 97–130.Google Scholar
[3] Cantini, A., A theory of formal truth arithmetically equivalent to ID1, The Journal of Symbolic Logic, vol. 55 (1990), pp. 244–259.Google Scholar
[4] Cieśliński, C., Deflationism, conservativeness and maximality, Journal of Philosophical Logic, vol. 36 (2007), pp. 695–705.Google Scholar
[5] Davidson, D., The folly of trying to define truth, Journal of Philosophy, vol. 93 (1996), pp. 263–278, reprinted in (S. Blackburn and K. Simmons, editors) Truth , Oxford University Press, Oxford, 1999, pp. 308–322.Google Scholar
[6] Feferman, S., Reflecting on incompleteness, handwritten notes, 03 1987, 39 pp.Google Scholar
[7] Feferman, S., Systems of predicative analysis, The Journal of Symbolic Logic, vol. 29 (1964), pp. 1–30.Google Scholar
[8] Feferman, S., Systems of predicative analysis, II: Representations of ordinals, The Journal of Symbolic Logic, vol. 33 (1968), pp. 193–220.CrossRefGoogle Scholar
[9] Feferman, S., Iterated inductive fixed-point theories: Application to Hancock's conjecture, Patras logic symposion (Metakides, G., editor), North-Holland, Amsterdam, 1982, pp. 171–196.Google Scholar
[10] Feferman, S., Hilbert's program relativized: Proof-theoretical and foundational reductions, The Journal of Symbolic Logic, vol. 53 (1988), pp. 364–384.CrossRefGoogle Scholar
[11] Feferman, S., Reflecting on incompleteness, The Journal of Symbolic Logic, vol. 56 (1991), pp. 1–49.Google Scholar
[12] Feferman, S., Does reductive proof theory have a viable rationale?, Erkenntnis, vol. 53 (2000), pp. 63–96.Google Scholar
[13] Feferman, S., Axioms for determinateness and truth, The Review of Symbolic Logic, vol. 1 (2008), pp. 204–217.CrossRefGoogle Scholar
[14] Friedman, H. and Sheard, M., An axiomatic approach toward self-referential truth, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 1–21.Google Scholar
[15] Hájek, P. and Pudlak, P., Metamathematics of first-order arithmetic, Springer, Berlin, 1993.Google Scholar
[16] Halbach, V., Axiomatic theories of truth, Stanford encyclopedia of philosophy, URL: http://plato.stanford.edu/entries/truth-axiomatic.Google Scholar
[17] Halbach, V., A system of complete and consistent truth, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 311–327.Google Scholar
[18] Halbach, V., Axiomatische Wahrheitstheorien, Akademie Verlag, Berlin, 1996.CrossRefGoogle Scholar
[19] Halbach, V., Conservative theories of classical truth, Studia Logica, vol. 62 (1999), pp. 353–370.Google Scholar
[20] Halbach, V., Truth and reduction, Erkenntnis, vol. 53 (2000), pp. 97–126.Google Scholar
[21] Halbach, V., Reducing compositional to disquotational truth, The Review of Symbolic Logic, vol. 2 (2009), pp. 786–798.Google Scholar
[22] Halbach, V., Axiomatic theories of truth, Cambridge University Press, Cambridge, forthcoming.Google Scholar
[23] Halbach, V. and Horsten, L., Axiomatizing Kripke's theory of truth, The Journal of Symbolic Logic, vol. 71 (2006), pp. 677–712.Google Scholar
[24] Kaye, R., Models of Peano Arithmetic, Clarendon Press, Oxford, 1991.CrossRefGoogle Scholar
[25] Ketland, J., Deflationism and Tarski's paradise, Mind, vol. 108 (1999), pp. 69–94.Google Scholar
[26] Kotlarski, H., Krajewski, S., and Lachlan, A.H., Construction of satisfaction classes for nonstandard models, Canadian Mathematical Bulletin, vol. 24 (1981), pp. 283–293.CrossRefGoogle Scholar
[27] Kripke, S., Outline of a theory of truth, Journal of Philosophy, vol. 72 (1975), pp. 690–716.Google Scholar
[28] Lachlan, A., Full satisfaction classes and recursive saturation, Canadian Mathematical Bulletin, vol. 24 (1981), pp. 295–297.Google Scholar
[29] Lindström, P., Aspects of incompleteness, 2nd ed., Lecture Notes in Logic, 10, A K Peters, Ltd, Massachusetts, 2003.Google Scholar
[30] McGee, V., How truthlike can a predicate be? Anegative result, Journal of Philosophical Logic, vol. 14 (1985), pp. 399–410.Google Scholar
[31] McGee, V., Maximal consistent sets of instances of Tarski's schema (T), Journal of Philosophical Logic, vol. 21 (1992), pp. 235–241.Google Scholar
[32] McGee, V., In praise of the free lunch: Why disquotationalists should embrace compositional semantics, Self-reference (Bolander, T. et al., editors), CSLI Publications, Stanford, 2006, pp. 95–120.Google Scholar
[33] Niebergall, K., On the logic of reducibility: Axioms and examples, Erkenntnis, vol. 53 (2000), pp. 27–61.Google Scholar
[34] Pohlers, W., Proof theory: The first step into impredicativity, Springer, Berlin, 2009.Google Scholar
[35] Rathjen, M., The role of parameters in bar rule and bar induction, The Journal of Symbolic Logic, vol. 56 (1991), pp. 715–730.Google Scholar
[36] Rathjen, M., The realm of ordinal analysis, Sets and proofs (Cooper, S. and Truss, J., editors), Cambridge University Press, Cambridge, 1999, pp. 219–279.Google Scholar
[37] Sheard, M., A guide to truth predicates in the modern era, The Journal of Symbolic Logic, vol. 59 (1994), pp. 1032–1054.CrossRefGoogle Scholar
[38] Simpson, S., Subsystems of second order arithmetic, Springer, Berlin, 1999.CrossRefGoogle Scholar
[39] Takeuti, G., Proof theory, 2nd ed., North-Holland, Amsterdam, 1987.Google Scholar
[40] Tarski, A., The semantic conception of truth and the foundation of semantics, Philosophy and Phenomenological Research, vol. 4 (1944), pp. 341–376, reprinted in (Tarski, A., editor) Alfred Tarski, Collected Paper 2 , Birkhauser, Basel, 1986, pp. 665–699.Google Scholar
[41] Tarski, A., The concept of truth in formalized languages, Logic, semantics, metamathematics (Tarski, A., editor), Hackett, Indianapolis, 2nd ed., 1983, pp. 152–278.Google Scholar