The Kim-Pillay theorem for Abstract Elementary Categories

Kamsma, Mark (2020) The Kim-Pillay theorem for Abstract Elementary Categories. Journal of Symbolic Logic. ISSN 0022-4812

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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.

Item Type: Article
Uncontrolled Keywords: dividing,accessible category,simple theory,abstract elementary class,independence relation,abstract elementary category,logic ,/dk/atira/pure/subjectarea/asjc/2600/2609
Faculty \ School: Faculty of Science > School of Mathematics
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Depositing User: LivePure Connector
Date Deposited: 29 Oct 2020 01:03
Last Modified: 17 Feb 2021 00:56
DOI: 10.1017/jsl.2020.75

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