Some characterization and preservation theorems in modal logic

Annals of Pure and Applied Logic 163 (12):1928-1939 (2012)
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Abstract

A class of Kripke models is modally definable if there is a set of modal formulas such that the class consists exactly of models on which every formula from that set is globally true. In this paper, a class is also considered definable if there is a set of formulas such that it consists exactly of models in which every formula from that set is satisfiable. The notion of modal definability is then generalized by combining these two. For thus obtained types of modal definability on the level of Kripke models, we give characterization theorems in the usual form, in terms of algebraic closure conditions. As some consequences of these, various preservation results are presented. Also, some characterizations are strengthened by replacing closure under ultraproducts with closure under ultrapowers

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Citations of this work

Existential Definability of Modal Frame Classes.Tin Perkov & Luka Mikec - 2020 - Mathematical Logic Quarterly 66 (3):316-325.

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References found in this work

Derivation Rules as Anti-Axioms in Modal Logic.Yde Venema - 1993 - Journal of Symbolic Logic 58 (3):1003-1034.
The Range of Modal Logic: An Essay in Memory of George Gargov.Johan van Benthem - 1999 - Journal of Applied Non-Classical Logics 9 (2):407-442.
The Range of Modal Logic: An Essay in Memory of George Gargov.Johan van Benthem - 1999 - Journal of Applied Non-Classical Logics 9 (2-3):407-442.

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