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The Kim-Pillay theorem for Abstract Elementary Categories

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Abstract

We introduce the framework of AECats (abstract elementary categories), generalising both the category of models of some first-order theory and the category of subsets of models. Any AEC and any compact abstract theory ("cat", as introduced by Ben-Yaacov) forms an AECat. In particular, we find applications in positive logic and continuous logic: the category of (subsets of) models of a positive or continuous theory is an AECat.

The Kim-Pillay theorem for first-order logic characterises simple theories by the properties dividing independence has. We prove a version of the Kim-Pillay theorem for AECats with the amalgamation property, generalising the first-order version and existing versions for positive logic.

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Original languageEnglish
JournalJournal of Symbolic Logic
Early online date30 Oct 2020
DOIs
Publication statusE-pub ahead of print - 30 Oct 2020
Peer-reviewedYes

Keywords

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  • dividing, accessible category, simple theory, abstract elementary class, independence relation, abstract elementary category

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ID: 184900776

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