This course aims to discuss at length mathematical structures used in semantical analysis of logic. These structures include topological spaces, posets and other relational structures, frames and locales of point-free topology, universal algebras (in particular, distributive lattices, Boolean algebras, Heyting algebras, modal algebras), categories, etc. We will study all these structures through the prism of modern logic.

We will study duality theories for Boolean algebras, Heyting algebras, distributive lattices, modal algebras and other algebraic structures appearing in logic. We will discuss the consequences of these results for corresponding logics in terms of completeness, the finite model property, axiomatizations, decidability, interpolation etc. The classes of intermediate, substructural, modal and other non-classical logics will also be considered. We will also pay special attention to topological models of logic and point-free topology.

Prerequisites

Basic skills in formal (mathematical reasoning). Familiarity with the basic systems of logic (propositional and first-order logics, modal logics) is not necessary, but would be helpful.

All the details about the course can be found on the course webpage.