Algebra Seminar talk
The Baire closure and its logic
In this talk, we consider semantics for modal logics based on the Baire quotient of a topological space, defined as the powerset algebra modulo the meager sets. We show that such algebras admit a natural closure operator satisfying the S5 axioms. Moreover, they enjoy a McKinsey and Tarski property in that they are complete for a wide class of spaces which includes e.g. all Euclidean spaces.
Finally, we show how Baire quotients can decimate the complexity of topological reasoning by showing that typically undecidable dynamic topological logics become decidable when evaluated on the Baire quotient.