Formal Model Theory & Higher Topology

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.

Very minor revision. The presentation has been improved. Submitted for publication

References in corpus (2)

• An informal introduction to topos theory
• General facts on the Scott Adjunction

Cited by in corpus (2)

• General facts on the Scott Adjunction
• Towards Higher Topology