Completeness of S4 with respect to the real line: revisited

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• 作者：Bezhanishvili ; Guram ; Gehrke ; Mai
• 关键词：03B45 ; 06E25 ; 54C10 ; Modal logic ; Topology ; Boolean algebras with operators ; Completeness
• 刊名：Annals of Pure and Applied Logic
• 出版年：2005
• 期刊代码：4_01680072
• 类别：cp
• 出版时间：January, 2005
• 卷：131
• 期：1-3
• 页码：287-301
• 文件大小：193 K

摘要

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 (Ann. of Math. (2) 45 (1944) 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 (J. Appl. Non-Classical Logics 9 (1999) 369).