The Mckinsey–Tarski Theorem for Locally Compact Ordered Spaces

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Bulletin of Symbolic Logic 27 (2):187-211 (2021)
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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.

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10.1017/bsl.2021.16

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Nick Bezhanishvili
University of Amsterdam

Citations of this work

A Model Theory of Topology.Paolo Lipparini - forthcoming - Studia Logica:1-35.

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References found in this work

Domain theory in logical form.Samson Abramsky - 1991 - Annals of Pure and Applied Logic 51 (1-2):1-77.
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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