Completeness of S4 with respect to the real line: revisited

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Annals of Pure and Applied Logic 131 (1-3):287-301 (2005)
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Abstract

We prove that S4 is complete with respect to Boolean combinations of countable unions of convex subsets of the real line, thus strengthening a 1944 result of McKinsey and Tarski 45 141). We also prove that the same result holds for the bimodal system S4+S5+C, which is a strengthening of a 1999 result of Shehtman 369).

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10.1016/j.apal.2004.06.003

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Citations of this work

Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.
Completeness of S4 for the Lebesgue Measure Algebra.Tamar Lando - 2012 - Journal of Philosophical Logic 41 (2):287-316.

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References found in this work

Modal Logics Between S 4 and S 5.M. A. E. Dummett & E. J. Lemmon - 1959 - Mathematical Logic Quarterly 5 (14‐24):250-264.
Modal Logics Between S 4 and S 5.M. A. E. Dummett & E. J. Lemmon - 1959 - Mathematical Logic Quarterly 5 (14-24):250-264.
« Everywhere » and « here ».Valentin Shehtman - 1999 - Journal of Applied Non-Classical Logics 9 (2-3):369-379.
Five critical modal systems.L. Esakia & V. Meskhi - 1977 - Theoria 43 (1):52-60.

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