0586675 - MÚ 2025 RIV US eng J - Journal Article
Di Liberti, Ivan
Formal model theory and higher topology.
Mathematical Logic Quarterly. Roč. 70, č. 1 (2024), s. 111-125. ISSN 0942-5616. E-ISSN 1521-3870
R&D Projects: GA ČR(CZ) GX20-31529X
Institutional support: RVO:67985840
Keywords : abstract elementary classes * categories
OECD category: Pure mathematics
Impact factor: 0.3, year: 2022
Method of publishing: Open access
https://doi.org/10.1002/malq.202300006

We study the 2-categories BIon, of (generalized) bounded ionads, and (Formula presented.), of accessible categories with directed colimits, as an abstract 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 abstract elementary classes to locally decidable topoi. We introduce the notion of categories of saturated objects and relate it to atomic topoi.
Permanent Link: https://hdl.handle.net/11104/0354104