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Rapport Année : 2022

Generalized Keisler Theorems for First-order Logic and Protologics

Résumé

The Keisler theorems dealing with the definability in first-order logic of classes of structures are generalized and adapted to non-classical logics. On the one hand, we generalize and prove by completely different means an analogue of the Keisler-Shelah isomorphism theorem for first-order logic and countable languages, where the notion of isomorphism is replaced in that theorem by a variant of partial isomorphism. On the other hand, we adapt the Keisler theorems for first-order logics to protologics, i.e. logics such that the truth conditions of their connectives are expressible by first-order formulas. Our results are based on similar theorems for atomic and molecular logics proved in a companion article [5]. We indeed show in this present article that first-order logic and protologics are as expressive as some atomic and molecular logics.
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Dates et versions

hal-03884245 , version 1 (05-12-2022)

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Paternité - Pas d'utilisation commerciale - Pas de modification

Identifiants

  • HAL Id : hal-03884245 , version 1

Citer

Guillaume Aucher. Generalized Keisler Theorems for First-order Logic and Protologics. Université de Rennes 1 (UR1). 2022. ⟨hal-03884245⟩
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