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 \(\mathsf S4\) 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.
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Acknowledgements
We are thankful to the referee who suggested to add Section 5 to the paper. The first two authors were partially supported by Shota Rustaveli National Science Foundation Grant # DI-2016-25.
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Bezhanishvili, G., Bezhanishvili, N., Lucero-Bryan, J. et al. A New Proof of the McKinsey–Tarski Theorem. Stud Logica 106, 1291–1311 (2018). https://doi.org/10.1007/s11225-018-9789-5
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DOI: https://doi.org/10.1007/s11225-018-9789-5