Some kinds of modal completeness

Studia Logica 39 (2-3):125 - 141 (1980)

Abstract
In the modal literature various notions of completeness have been studied for normal modal logics. Four of these are defined here, viz. (plain) completeness, first-order completeness, canonicity and possession of the finite model property — and their connections are studied. Up to one important exception, all possible inclusion relations are either proved or disproved. Hopefully, this helps to establish some order in the jungle of concepts concerning modal logics. In the course of the exposition, the interesting properties of first-order definability and preservation under ultrafilter extensions are introduced and studied as well
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DOI 10.1007/BF00370316
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References found in this work BETA

A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
An Incomplete Logic Containing S.Kit Fine - 1974 - Theoria 40 (1):23-29.
An Introduction to Modal Logic.E. J. Lemmon, Dana Scott & Krister Segerberg - 1979 - Journal of Symbolic Logic 44 (4):653-654.

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Citations of this work BETA

Varieties of Complex Algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
Topology and Duality in Modal Logic.Giovanni Sambin & Virginia Vaccaro - 1988 - Annals of Pure and Applied Logic 37 (3):249-296.
Atom Structures of Cylindric Algebras and Relation Algebras.Ian Hodkinson - 1997 - Annals of Pure and Applied Logic 89 (2):117-148.
The McKinsey Axiom is Not Canonical.Robert Goldblatt - 1991 - Journal of Symbolic Logic 56 (2):554-562.
On Axiomatising Products of Kripke Frames.Ágnes Kurucz - 2000 - Journal of Symbolic Logic 65 (2):923-945.

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