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arXiv · 2010.00319

Formal Model Theory & Higher Topology

Ivan Di Liberti
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Abstract

We study the $2$-categories BIon, of (generalized) bounded ionads, and $\text{Acc}_\omega$, 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.

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Ivan Di Liberti. 2020-09-29. Formal Model Theory & Higher Topology. https://doi.org/10.1002/malq.202300006

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