Existential definability of modal frame classes

A class of Kripke frames is called modally definable if there is a set of modal formulas such that the class consists exactly of frames on which every formula from that set is valid, i. e. globally true under any valuation. Here, existential definability of Kripke frame classes is defined analogously, by demanding that each formula from a defining set is satisfiable under any valuation. This is equivalent to the definability by the existential fragment of modal language enriched with the universal modality. A model theoretic characterization of this type of definability is given.

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