Review of Symbolic Logic 6 (3):545-570 (2013)

Philip Kremer
University of Toronto at Scarborough
In the topological semantics for modal logic, S4 is well-known to be complete for the rational line, for the real line, and for Cantor space: these are special cases of S4’s completeness for any dense-in-itself metric space. The construction used to prove completeness can be slightly amended to show that S4 is not only complete, but also strongly complete, for the rational line. But no similarly easy amendment is available for the real line or for Cantor space and the question of strong completeness for these spaces has remained open, together with the more general question of strong completeness for any dense-in-itself metric space. In this paper, we prove that S4 is strongly complete for any dense-in-itself metric space
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DOI 10.1017/s1755020313000087
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References found in this work BETA

An Ascending Chain of S4 Logics.Kit Fine - 1974 - Theoria 40 (2):110-116.
On Some Completeness Theorems in Modal Logic.D. Makinson - 1966 - Mathematical Logic Quarterly 12 (1):379-384.
Diodorean Modality in Minkowski Spacetime.Robert Goldblatt - 1980 - Studia Logica 39 (2-3):219 - 236.

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Citations of this work BETA

First Order S4 and its Measure-Theoretic Semantics.Tamar Lando - 2015 - Annals of Pure and Applied Logic 166 (2):187-218.
Quantified Modal Logic on the Rational Line.Philip Kremer - 2014 - Review of Symbolic Logic 7 (3):439-454.
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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