X-2015-01: Lauridsen, Frederik Möllerström (2015) Bitopological Vietoris spaces and positive modal logic. [Report]
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Abstract
Using the isomorphism from Bezhanishvili et al. 2010 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 from Bezhanishvili & Kurz 2007, Palmigiano 2004, Venema & Vosmaer 2014. 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.
| Item Type: | Report |
|---|---|
| Report Nr: | X-2015-01 |
| Series Name: | Technical Notes (X) Series |
| Year: | 2015 |
| Uncontrolled Keywords: | bitopology, Vietoris construction, positive modal logic, coalgebraic semantics, pairwise Stone spaces |
| Subjects: | Logic |
| Date Deposited: | 12 Oct 2016 14:38 |
| Last Modified: | 12 Oct 2016 14:38 |
| URI: | https://eprints.illc.uva.nl/id/eprint/692 |
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