Disjunctions with stopping conditions

Bulletin of Symbolic Logic 27 (3):231-253 (2021)
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Abstract

We introduce a tool for analysing models of $\text {CT}^-$, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan’s theorem that the arithmetical part of models of $\text {CT}^-$ are recursively saturated. We also use this tool to provide a new proof of theorem from [8] that all models of $\text {CT}^-$ carry a partial inductive truth predicate. Finally, we construct a partial truth predicate defined for a set of formulae whose syntactic depth forms a nonstandard cut which cannot be extended to a full truth predicate satisfying $\text {CT}^-$.

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Roman Kossak
City University of New York

Citations of this work

Full Satisfaction Classes, Definability, and Automorphisms.Bartosz Wcisło - 2022 - Notre Dame Journal of Formal Logic 63 (2):143-163.

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References found in this work

Truth, disjunction, and induction.Ali Enayat & Fedor Pakhomov - 2019 - Archive for Mathematical Logic 58 (5-6):753-766.
Models of weak theories of truth.Mateusz Łełyk & Bartosz Wcisło - 2017 - Archive for Mathematical Logic 56 (5-6):453-474.
Nonstandard definability.Stuart T. Smith - 1989 - Annals of Pure and Applied Logic 42 (1):21-43.
Bounded Induction and Satisfaction Classes.Henryk Kotlarski - 1986 - Mathematical Logic Quarterly 32 (31-34):531-544.

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