Stone duality and strong conceptual completeness for infinitary logic

Abstract: The classical Stone duality, applied to the Lindenbaum-Tarski algebra of a propositional theory, allows the syntax of the theory to be canonically recovered from its space of models; this encompasses both the completeness and definability theorems for propositional logic. Many known variants and generalizations of Stone duality have analogous interpretations as completeness-definability theorems for various fragments of finitary propositional and first-order logic. In this talk, I will give an overview of this duality-theoretic approach to completeness, including the key examples of Stone duality as well as Makkai duality for first-order logic. I will then present a duality theorem for the countably infinitary first-order logic $L_{\omega_1\omega}$, proved using tools from invariant descriptive set theory as well as topos theory.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic