Formal Model Theory & Higher Topology

Abstract

We study the 2-categories of (generalized) bounded ionads BIon and accessible categories with directed colimits Accω 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, and categories of saturated objects to atomic topoi. Contents