## A question about modal logic

September 5, 2008Say that a class of Kripke frames, , is **compact **just in case, for every set of propositional modal formulae, , has a model in (i.e. a model based on a frame in ) iff every finite subset of has a model in .

We know some sufficient conditions for to be compact, for example, if is closed under taking ultraproducts. Does anyone know any necessary conditions (or even necessary and sufficient conditions) for compactness in this sense?

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