0586675 - MÚ 2025 RIV US eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GX20-31529X
Institucionální podpora: RVO:67985840
Klíčová slova: abstract elementary classes * categories
Obor OECD: Pure mathematics
Impakt faktor: 0.3, rok: 2022
Způsob publikování: 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.
Trvalý link: https://hdl.handle.net/11104/0354104