A new proof of the McKinsey-Tarski Theorem
Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan, Jan van Mill
Abstract:
It is a landmark theorem of McKinsey and Tarski that if we interpret modal diamond as closure (and hence modal box as interior), then S4 is the logic of any dense-in-itself metrizable space. The McKinsey-Tarski Theorem relies heavily on a metric that gives rise to the topology. We give a new and more topological proof of the theorem, utilizing Bing's Metrization Theorem.