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Strong Completeness of Modal Logics Over 0-Dimensional Metric Spaces
Review of Symbolic Logic 13 (3):611-632 (2020)
Abstract
We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for some languages and spaces, no standard modal deductive system is strongly complete.My notes
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References found in this work
Some theorems about the sentential calculi of Lewis and Heyting.J. C. C. McKinsey & Alfred Tarski - 1948 - Journal of Symbolic Logic 13 (1):1-15.
Models and Ultraproducts: An Introduction.J. L. Bell & A. B. Slomson - 1972 - Journal of Symbolic Logic 37 (4):763-764.
Strong completeness of s4 for any dense-in-itself metric space.Philip Kremer - 2013 - Review of Symbolic Logic 6 (3):545-570.
Modal logics of metric spaces.Guram Bezhanishvili, David Gabelaia & Joel Lucero-Bryan - 2015 - Review of Symbolic Logic 8 (1):178-191.
Spatial logic of tangled closure operators and modal mu-calculus.Robert Goldblatt & Ian Hodkinson - 2017 - Annals of Pure and Applied Logic 168 (5):1032-1090.
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