Bitopological Vietoris spaces and positive modal logic
نویسنده
چکیده
Using the isomorphism from [3] between the category Pries of Priestley spaces and the category PStone of pairwise Stone spaces we construct a Vietoris hyperspace functor on the category PStone related to the Vietoris hyperspace functor on the category Pries [4, 18, 24]. We show that the coalgebras for this functor determine a semantics for the positive fragment of modal logic. The sole novelty of the present work is the explicit construction of the Vietoris hyperspace functor on the category PStone as well as the phrasing of otherwise well-known results in a bitopological language. ∗This constitutes the final report for a individual project under the supervision of Nick Bezhanishvili at the Institute of Logic, Language and Computation. †[email protected]
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