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  • GRAHAM E. LEIGH (a1)


We present a cut elimination argument that witnesses the conservativity of the compositional axioms for truth (without the extended induction axiom) over any theory interpreting a weak subsystem of arithmetic. In doing so we also fix a critical error in Halbach’s original presentation. Our methods show that the admission of these axioms determines a hyper-exponential reduction in the size of derivations of truth-free statements.



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[1]Barwise, J., Admissible Sets and Structures: An Approach to Definability Theory, Springer–Verlag, Berlin, 1975.
[2]Enayat, A. and Visser, A., Full satisfaction classes in a general setting (Part 1), unpublished manuscript, 2012.
[3]Enayat, A. and Visser, A., New constructions of satisfaction classes, Unifying the philosophy of truth (Achourioti, T., Galinon, H., Fujimoto, K. and Martínez-Fernández, J., editors), in press.
[4]Feferman, S., Reflecting on incompleteness, this Journal, vol. 56 (1991), pp. 149.
[5]Fischer, M., Minimal truth and interpretability. Review of Symbolic Logic, vol. 2 (2009), no. 4, pp. 799815.
[6]Friedman, H. and Sheard, M., An Axiomatic Approach to Self-Referential Truth. Annals of Pure and Applied Logic, vol. 33 (1987), pp. 121.
[7]Halbach, V., Conservative theories of classical truth. Studia Logica, vol. 62 (1999), pp. 353370.
[8]Halbach, V., Axiomatic theories of truth, Cambridge University Press, Cambridge, 2011.
[9]Halbach, V., Axiomatic theories of truth, second edition. Cambridge University Press, Cambridge, 2014.
[10]Halbach, V. and Leigh, G. E., Axiomatic theories of truth (Zalta, E. N., editors), The Stanford Encyclopedia of Philosophy (Summer 2014 Edition), url
[11]Krajewski, S., Nonstandard satisfaction classes, Set Theory and Hierarchy Theory: A Memorial Tribute to Andrzej Mostowski (Marek, W. et al. , editors), Lecture Notes in Mathematics, vol. 537, Springer-Verlag, Berlin, 1976, pp. 121144.
[12]Kotlarski, H., Bounded Induction and Satisfaction Classes. Zeitschrift für Mathematische Logik, vol. 32 (1986), pp. 531–44.
[13]Kotlarski, H., Krajewski, S., and Lachlan, A. H., Construction of satisfaction classes for nonstandard models. Canadian Mathematical Bulletin, vol. 24 (1981), pp. 283–93.
[14]Leigh, G. E., A proof-theoretic account of classical principles of truth. Annals of Pure and Applied Logic, vol. 164 (2013), pp. 10091024.
[15]Leigh, G. E. and Rathjen, M., An ordinal analysis for theories of self-referential truth. Archive for Mathematical Logic, vol. 49 (2010), no. 2, pp. 213247.
[16]Leigh, G. E. and Rathjen, M., The Friedman-Sheard programme in intuitionistic logic, this Journal, vol. 77 (2012), no. 3, pp. 777806.



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