THE MCKINSEY–TARSKI THEOREM FOR LOCALLY COMPACT ORDERED SPACES
Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero‐Bryan, Jan VAN MILL · Bulletin of Symbolic Logic · 2021
Abstract We prove that the modal logic of a crowded locally compact generalized ordered space is $\textsf {S4}$ . This provides a version of the McKinsey–Tarski theorem for generalized ordered spaces. We then utilize this theorem to axiomatize the modal logic of an arbitrary locally compact generalized ordered space.