Modal definability in topology
David Gabelaia

Abstract:
This thesis is mainly concerned with the definability issue when modal
logic is interpreted on topological spaces. A topological analogon of
Goldblatt-Thomason theorem is proved. Some new topological
constructions are introduced. One of them, namely the notion of
compact extension, is a generalization of the concept of Stone-Cech
compactification known in topology. The preservation of modal validity
with respect to suitable topological operations is presented.

Keywords: Modal Logic, semantics, topology, definability.