Canonical modal logics and ultrafilter extensions

DOI10.2307/2273696zbMath0405.03011OpenAlexW2136147947MaRDI QIDQ4190614

J. F. A. K. van Benthem

Publication date: 1979

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2273696

zbMATH Keywords

Possible WorldsModel TheoryKripke SemanticsCononical Modal LogicFirst-Order Definable Complete Modal LogicsKripke FrameModal AlgebrasUltrafilter Extension

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Modal logic (including the logic of norms) (03B45) Ultraproducts and related constructions (03C20)

Related Items (13)

Modal definability based on Łukasiewicz validity relations ⋮ Topology and duality in modal logic ⋮ Varieties of complex algebras ⋮ Mixed algebras and their logics ⋮ Preservation and reflection of bisimilarity via invertible steps ⋮ Some kinds of modal completeness ⋮ Book review of: B. Liao (ed.) et al., Dynamics, uncertainty and reasoning ⋮ A Road to Ultrafilter Extensions ⋮ On ultrafilter extensions of first-order models and ultrafilter interpretations ⋮ Frame constructions, truth invariance and validity preservation in many-valued modal logic ⋮ Modal logic with names ⋮ A simple incomplete extension of T which is the union of two complete modal logics with f. m. p ⋮ On measure quantifiers in first-order arithmetic

Cites Work

• Modal formulas are either elementary or not ΣΔ-elementary
• An incomplete logic containing S4
• An incompleteness theorem in modal logic

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