Topological Modal Logics Satisfying Finite Chain Conditions

Abstract

We modify the semantics of topological modal logic, a language due to Moss and Parikh. This enables us to study the corresponding theory of further classes of subset spaces. In the paper we deal with spaces where every chain of opens fulfils a certain finiteness condition. We consider both a local finiteness condition relevant to points and a global one concerning the whole frame. Completeness of the appearing logical systems, which turn out to be generalizations of the well-known modal system G, can be obtained in the same manner as in the case of the general subset space logic. It is our main purpose to show that the systems differ with regard to the finite model property.