The modal logic of stone spaces: Diamond as derivative
Review of Symbolic Logic 3 (1):26-40 (2010)
| Abstract | We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces is K4 and the modal logic of weakly scattered Stone spaces is K4G. As a corollary, we obtain that K4 is also the modal logic of compact Hausdorff spaces and K4G is the modal logic of weakly scattered compact Hausdorff spaces. | |||||||||
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