On Cut-Elimination Arguments for Axiomatic Theories of Truth

Studia Logica 110 (3):785-818 (2022)
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Abstract

As is mentioned in Leigh :845-865, 2015), it is an open problem whether for several axiomatic theories of truth, including Friedman–Sheard theory \ and Kripke–Feferman theory \ :690-716, 1976), there exist cut-elimination arguments that give the upper bounds of their proof-theoretic strengths. In this paper, we give complete cut-elimination results for several well-known axiomatic theories of truth. In particular, we treat the systems \, and \ \\) of Friedman and Sheard’s theories and \.

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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Reflecting on incompleteness.Solomon Feferman - 1991 - Journal of Symbolic Logic 56 (1):1-49.
Notes on Formal Theories of Truth.Andrea Cantini - 1989 - Zeitshrift für Mathematische Logik Und Grundlagen der Mathematik 35 (1):97--130.
A theory of formal truth arithmetically equivalent to ID.Andrea Cantini - 1990 - Journal of Symbolic Logic 55 (1):244 - 259.
Notes on Formal Theories of Truth.Andrea Cantini - 1989 - Mathematical Logic Quarterly 35 (2):97-130.

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