The Kim-Pillay theorem for Abstract Elementary Categories

Kamsma, Mark (2020) The Kim-Pillay theorem for Abstract Elementary Categories. Journal of Symbolic Logic, 85 (4). pp. 1717-1741. ISSN 0022-4812

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Abstract

We introduce the framework of AECats (abstract elementary categories), generalizing 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 characterizes simple theories by the properties dividing independence has. We prove a version of the Kim-Pillay theorem for AECats with the amalgamation property, generalizing 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
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 29 Oct 2020 01:03
Last Modified: 12 Jun 2021 11:49
URI: https://ueaeprints.uea.ac.uk/id/eprint/77462
DOI: 10.1017/jsl.2020.75

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