On the theories classified by an \'etendue
Joshua Wrigley
TL;DR
This paper provides a model-theoretic characterization of geometric theories classified by étendues, showing how models are determined by specific formulae witnesses, bridging syntax and semantics in topos theory.
Contribution
It introduces a new model-theoretic framework for understanding theories classified by étendues, connecting localic topoi with syntactic and semantic model properties.
Findings
Models are uniquely determined by witnesses of certain formulae.
Provides a bridge between topos theory and model theory.
Characterizes locally localic topoi via model-theoretic conditions.
Abstract
We give a model-theoretic characterisation of the geometric theories classified by \'etendues -- the `locally localic' topoi. They are the theories where each model is determined, syntactically and semantically, by any witness of a fixed collection of formulae.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Mathematical and Theoretical Analysis