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Notes on bounded induction for the compositional truth predicate
Review of Symbolic Logic 10 (3):455-480 (2017)
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.Author's Profile
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Citations of this work
The Function of Truth and the Conservativeness Argument.Kentaro Fujimoto - 2022 - Mind 131 (521):129-157.
Truth, disjunction, and induction.Ali Enayat & Fedor Pakhomov - 2019 - Archive for Mathematical Logic 58 (5-6):753-766.
Local collection and end-extensions of models of compositional truth.Mateusz Łełyk & Bartosz Wcisło - 2021 - Annals of Pure and Applied Logic 172 (6):102941.
The Implicit Commitment of Arithmetical Theories and Its Semantic Core.Carlo Nicolai & Mario Piazza - 2019 - Erkenntnis 84 (4):913-937.
References found in this work
Relative truth definability of axiomatic truth theories.Kentaro Fujimoto - 2010 - Bulletin of Symbolic Logic 16 (3):305-344.
Conservativity for theories of compositional truth via cut elimination.Graham E. Leigh - 2015 - Journal of Symbolic Logic 80 (3):845-865.
Metamathematics of First-Order Arithmetic.Petr Hajék & Pavel Pudlák - 1994 - Studia Logica 53 (3):465-466.
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