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Truth and Collection
Journal of Symbolic Logic:1-26 (forthcoming)
Abstract
Answering a question of Kaye, we show that the compositional truth theory with the full collection scheme is conservative over Peano Arithmetic. We demonstrate it by showing that countable models of compositional truth which satisfy the internal induction or collection axioms can be end-extended to models of the respective theory.Other Versions
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Citations of this work
Satisfaction Classes with Approximate Disjunctive Correctness.Ali Enayat - 2025 - Review of Symbolic Logic 18 (2):545-562.
Saturation properties for compositional truth with propositional correctness.Bartosz Wcisło - 2025 - Annals of Pure and Applied Logic 176 (2):103512.
References found in this work
Conservativity for theories of compositional truth via cut elimination.Graham E. Leigh - 2015 - Journal of Symbolic Logic 80 (3):845-865.
Disjunctions with Stopping Conditions.Roman Kossak & Bartosz Wcisło - 2021 - Bulletin of Symbolic Logic 27 (3):231-253.
Local collection and end-extensions of models of compositional truth.Mateusz Łełyk & Bartosz Wcisło - 2021 - Annals of Pure and Applied Logic 172 (6):102941.
Deflationary Truth and Pathologies.Cezary Cieśliński - 2010 - Journal of Philosophical Logic 39 (3):325-337.
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