Incompleteness results in Kripke semantics

Journal of Symbolic Logic 56 (2):517-538 (1991)
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Abstract

By means of models in toposes of C-sets (where C is a small category), necessary conditions are found for the minimum quantified extension of a propositional (intermediate, modal) logic to be complete with respect to Kripke semantics; in particular, many well-known systems turn out to be incomplete

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Citations of this work

First-order intensional logic.Melvin Fitting - 2004 - Annals of Pure and Applied Logic 127 (1-3):171-193.
First-order classical modal logic.Horacio Arló-Costa & Eric Pacuit - 2006 - Studia Logica 84 (2):171 - 210.
Why Combine Logics?Patrick Blackburn & Maarten de Rijke - 1997 - Studia Logica 59 (1):5 - 27.

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References found in this work

Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
An ascending chain of S4 logics.Kit Fine - 1974 - Theoria 40 (2):110-116.
That All Normal Extensions of S4.3 Have the Finite Model Property.R. A. Bull - 1966 - Mathematical Logic Quarterly 12 (1):341-344.
Toposes and Local Set Theories. An Introduction.J. L. Bell - 1990 - Journal of Symbolic Logic 55 (2):886-887.

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