A New Proof of the McKinsey–Tarski Theorem

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Studia Logica 106 (6):1291-1311 (2018)
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Abstract

It is a landmark theorem of McKinsey and Tarski that if we interpret modal diamond as closure, then \ 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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10.1007/s11225-018-9789-5

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Nick Bezhanishvili
University of Amsterdam

Citations of this work

The Baire Closure and its Logic.G. Bezhanishvili & D. Fernández-Duque - 2024 - Journal of Symbolic Logic 89 (1):27-49.

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References found in this work

Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
Completeness of S4 with respect to the real line: revisited.Guram Bezhanishvili & Mai Gehrke - 2004 - Annals of Pure and Applied Logic 131 (1-3):287-301.
Modal Logics of Metric Spaces.Guram Bezhanishvili, David Gabelaia & Joel Lucero-Bryan - 2015 - Review of Symbolic Logic 8 (1):178-191.

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