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Truth, Logic and Invariance

Abstract : In the spirit of Klein's Erlanger program logical notions have been characterized as the invariant of some suitably motivated similarity relations S over structures. Not every authors agree on a choice of a similarity relation (e.g., Tarski [3], Feferman [2], Bonnay [1]) but one might argue that any plausible candidate should abide by a constraint of closure under definability: every operator which is definable in a language L whose logical constants are interpreted by S-invariant operators should be S-invariant. If L is a logic, being generated by a similarity relation closed under definability amounts to a kind of functional completeness of L with respect to a target notion of logicality. On the other hand we can define alethic extensions of a given model-theoretic logic L as the logics that one may obtain from L by adding to it the expressive power of an interpreted Tarskian truth predicate. We say that a logic L is truth-complete if every class of structures which is elementary (i.e., definable by one sentence) in an alethic extension of L is elementary in L. Eventually, we prove the following: a logic is truth complete if and only if it is generated by a similarity relation which is closed under definability.
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https://halshs.archives-ouvertes.fr/halshs-00792019
Contributor : Henri Galinon <>
Submitted on : Thursday, February 21, 2013 - 2:02:00 PM
Last modification on : Thursday, March 4, 2021 - 8:46:03 AM

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  • HAL Id : halshs-00792019, version 1

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Henri Galinon, Denis Bonnay, Julien Boyer. Truth, Logic and Invariance. Logic Colloquium '08 (2008 European summer meeting of the Association for Symbolic Logic), Jul 2008, Bern, Suisse. ⟨halshs-00792019⟩

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