Ultraproducts and possible worlds semantics in institutions. (abstract)

We develop possible worlds (Kripke) semantics at the categorical abstract model theoretic level provided by the so-called `institutions'.

Our general abstract modal logic framework provides a method for systematic Kripke semantics extensions of logical systems from computing science and logic.

We also extend the institution-independent method of ultraproducts of Ultraproducts in institutions to possible worlds semantics and prove a fundamental preservation result for abstract modal satisfaction.

As a consequence we develop a generic compactness result for possible worlds semantics.

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