Notes on bounded induction for the compositional truth predicate

Review of Symbolic Logic 10 (3):455-480 (2017)
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Abstract

We prove that the theory of the extensional compositional truth predicate for the language of arithmetic with \Delta 0 -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.

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Citations of this work

Axiomatic Theories of Truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.
Truth, Disjunction, and Induction.Ali Enayat & Fedor Pakhomov - 2019 - Archive for Mathematical Logic 58 (5-6):753-766.
On the Logicality of Truth.Kentaro Fujimoto - 2022 - Philosophical Quarterly 72 (4):853-874.

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References found in this work

Relative Truth Definability of Axiomatic Truth Theories.Kentaro Fujimoto - 2010 - Bulletin of Symbolic Logic 16 (3):305-344.
Bounded Induction and Satisfaction Classes.Henryk Kotlarski - 1986 - Mathematical Logic Quarterly 32 (31-34):531-544.

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