Year: 2020
Type: article
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.
Source: Journal of Symbolic Logic
DOI: 10.1017/jsl.2020.75
Author: MARK KAMSMA
Institution: University of East Anglia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3007429083