The McKinsey-Tarski theorem for locally compact ordered spaces
Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan, Jan van Mill

Abstract:
We prove that the modal logic of a crowded locally compact generalized ordered space is 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.