THE MODAL LOGIC OF STONE SPACES: DIAMOND AS DERIVATIVE
Guram Bezhanishvili, Leo Esakia, David Gabelaia · The Review of Symbolic Logic · 2010
We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces isK4and the modal logic of weakly scattered Stone spaces isK4G. As a corollary, we obtain thatK4is also the modal logic of compact Hausdorff spaces andK4Gis the modal logic of weakly scattered compact Hausdorff spaces.