Topological Product of Modal Logics with the McKinsey Axiom

Abstract

We consider products of modal logics in topological semantics and prove that the topological product of S4.1 and S4 is the fusion of logics S4.1 and S4 plus one extra asiom. This is an example of a topological product of logics that is greater than the fusion but less than the semiproduct of the corresponding logics. We also show that this product is decidable.