First-order definability in modal logic

Journal of Symbolic Logic 40 (1):35-40 (1975)
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Abstract

It is shown that a formula of modal propositional logic has precisely the same models as a sentence of the first-order language of a single dyadic predicate iff its class of models is closed under ultraproducts. as a corollary, any modal formula definable by a set of first-order conditions is always definable by a single such condition. these results are then used to show that the formula (lmp 'validates' mlp) is not first-order definable

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10.2307/2272267

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Citations of this work

Varieties of complex algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
Mathematical modal logic: A view of its evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.

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References found in this work

An ascending chain of S4 logics.Kit Fine - 1974 - Theoria 40 (2):110-116.
Decidability of S4.1.Krister Segerberg - 1968 - Theoria 34 (1):7-20.

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