In this talk we will delve into the background details of the previous talk by introducing syntactic proof systems and their categorical semantics, including the construction of syntactic categories and κ-classifying toposes, as well as the role of certain properties of Grothendieck topologies and
Kripke-Joyal semantics. We will then study some topos-theoretic completeness theorems for certain infinitary logics that generalize results of Deligne and Joyal.
This video is part of Masaryk University‘s Algebra seminar.
