Incompleteness results in Kripke semantics

Journal of Symbolic Logic 56 (2):517-538 (1991)
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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    Melvin Fitting (2004). First-Order Intensional Logic. Annals of Pure and Applied Logic 127 (1-3):171-193.
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