Completeness of S4 with respect to the real line: revisited

DOI10.1016/j.apal.2004.06.003zbMath1066.03032OpenAlexW1979519099MaRDI QIDQ705542

Mai Gehrke, Guram Bezhanishvili

Publication date: 31 January 2005

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2004.06.003

zbMATH Keywords

Cantor setBoolean algebras with operatorsCompletenessModal logicTopological completeness of S4

Mathematics Subject Classification ID

Special maps on topological spaces (open, closed, perfect, etc.) (54C10) Modal logic (including the logic of norms) (03B45) Boolean algebras with additional operations (diagonalizable algebras, etc.) (06E25)

Related Items (19)

A sound and complete axiomatization for Dynamic Topological Logic ⋮ Tree-like constructions in topology and modal logic ⋮ CONDITIONAL LOGIC IS COMPLETE FOR CONVEXITY IN THE PLANE ⋮ Topological Semantics of Justification Logic ⋮ Topology and measure in logics for region-based theories of space ⋮ Completeness of \(\mathrm S4\) for the Lebesgue measure algebra ⋮ Tarski's theorem on intuitionistic logic, for polyhedra ⋮ Modal logics of Stone spaces ⋮ MacNeille transferability and stable classes of Heyting algebras ⋮ Non-finite axiomatizability of dynamic topological logic ⋮ Modal logic axioms valid in quotient spaces of finite CW-complexes and other families of topological spaces ⋮ A new proof of the McKinsey-Tarski theorem ⋮ Connected modal logics ⋮ Dynamic measure logic ⋮ THE MCKINSEY–TARSKI THEOREM FOR LOCALLY COMPACT ORDERED SPACES ⋮ The modal logic of \({\beta(\mathbb{N})}\) ⋮ TOPOLOGICAL COMPLETENESS OF LOGICS ABOVE S4 ⋮ Hybrid logics of separation axioms ⋮ Strong Completeness of S4 for the Real Line

Cites Work

• Euclidean hierarchy in modal logic
• A problem in connected finite closure algebras
• The algebra of topology
• A Characterization of the Classes of Finite Tree Frames Which are Adequate for the Intuitionistic Logic
• Using the Universal Modality: Gains and Questions
• Five critical modal systems
• « Everywhere » and « here »
• Reasoning About Space: The Modal Way
• Modal Logics Between S 4 and S 5
• Some theorems about the sentential calculi of Lewis and Heyting
• Boolean Algebras with Operators. Part I
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