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Games for Truth

Published online by Cambridge University Press:  15 January 2014

P. D. Welch
P. D. Welch*
Affiliation:
School of Mathematics, University of Bristol, Bristol, BS8 1TW, UKE-mail: [email protected], URL: www.maths.bristol.ac.uk/~mapdw
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Abstract

We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of .

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 15 , Issue 4 , December 2009 , pp. 410 - 427
Copyright
Copyright © Association for Symbolic Logic 2009

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References

REFERENCES

[1] Burgess, J. P., The truth is never simple, The Journal for Symbolic Logic, vol. 51 (1986), no. 3, pp. 663–681.CrossRefGoogle Scholar
[2] Cantini, A., A theory of formal truth arithmetically equivalent to ID1 , The Journal for Symbolic Logic, vol. 55 (1990), no. 1, pp. 244–259.CrossRefGoogle Scholar
[3] Field, H., A revenge-immune solution to the semantic paradoxes, Journal of Philosophical Logic, vol. 32 (2003), no. 3, pp. 139–177.Google Scholar
[4] Friedman, H., Higher set theory and mathematical practice, Annals of Mathematical Logic, vol. 2 (1970), no. 3, pp. 325–327.Google Scholar
[5] Halbach, V. and Horsten, L., Axiomatising Kripke's Theory of Truth, The Journal for Symbolic Logic, vol. 71 (2006), no. 1, pp. 677–712.Google Scholar
[6] Herzberger, H.G., Naive semantics and the Liar paradox, Journal of Philosophy, vol. 79 (1982), pp. 479–497.CrossRefGoogle Scholar
[7] Herzberger, H.G., Notes on naive semantics, Journal of Philosophical Logic, vol. 11 (1982), pp. 61–102.CrossRefGoogle Scholar
[8] Leitgeb, H., What truth depends on, Journal of Philosophical Logic, vol. 34 (2005), pp. 155–192.Google Scholar
[9] Kechris, A. S., On Spector classes, Cabal seminar 76–77, (Kechris, A. S. and Moschovakis, Y. N., editors), Lecture Notes in Mathematics Series, vol. 689, Springer, 1978, pp. 245–278.CrossRefGoogle Scholar
[10] Kripke, S., Outline of a theory of truth, Journal of Philosophy, vol. 72 (1975), pp. 690–716.Google Scholar
[11] Martin, D. A., Revision and its rivals, Philosophical Issues, vol. 8 (1997), pp. 407–418.Google Scholar
[12] McGee, V., Truth, vagueness, and paradox: An essay on the logic of truth, Hackett, 1991.Google Scholar
[13] MedSalem, M. O. and Tanaka, K., -determinacy, comprehension and induction, The Journal for Symbolic Logic, vol. 72 (2007), no. 2, pp. 452–462.Google Scholar
[14] Moschovakis, Y., Elementary induction on abstract structures, Studies in Logic and the Foundations of Mathematics, vol. 77, North-Holland, Amsterdam, 1974.Google Scholar
[15] Welch, P. D., Ultimate truth vis à vis stable truth , Review of Symbolic Logic, vol. 1 (2008), no. 1, pp. 126–142.Google Scholar
[16] Welch, P. D., Weak systems of determinacy and arithmetical quasi-inductive definitions, submitted, arXiv:0905.4412.Google Scholar
[17] Yablo, S., Truth and reflection, Journal of Philosophical Logic, vol. 14 (1985), pp. 297–349.Google Scholar