Completeness of S4 with respect to the real line: revisited

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).

• Type: Journal
• Year: 2005
• Where: APAL
• Authors: Guram Bezhanishvili, Mai Gehrke
• Keywords: APAL 2005, Boolean Combinations, Convex Subsets, Countable Unions