Formal model theory and higher topology

We study the 2‐categories BIon, of (generalized) bounded ionads, and Accω$\text{Acc}_\omega$, of accessible categories with directed colimits, as an framework to approach formal model theory. We relate them to topoi and (lex) geometric sketches, which serve as categorical specifications of geometric...

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Bibliographic Details
Published in:Mathematical logic quarterly 2024-02, Vol.70 (1), p.111-125
Main Author: Di Liberti, Ivan
Format: Article
Language:English
Subjects:
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Sketches
Topology
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Summary:We study the 2‐categories BIon, of (generalized) bounded ionads, and Accω$\text{Acc}_\omega$, of accessible categories with directed colimits, as an framework to approach formal model theory. We relate them to topoi and (lex) geometric sketches, which serve as categorical specifications of geometric theories. We provide reconstruction and completeness‐like results. We relate elementary classes to locally decidable topoi. We introduce the notion of categories of saturated objects and relate it to atomic topoi.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.202300006