Axiomatic Classes of Intuitionistic Models

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dc.creatorGoldblatt,Robert
dc.date2005
dc.date.accessioned2024-02-06T12:54:03Z
dc.date.available2024-02-06T12:54:03Z
dc.descriptionA class of Kripke models for intuitionistic propositional logic is 'axiomatic' if it is the class of all models of some set of formulas (axioms). This paper discusses various structural characterisations of axiomatic classes in terms of closure under certain constructions, including images of bisimulations, disjoint unions, ultrapowers and 'prime extensions'. The prime extension of a model is a new model whose points are the prime filters of the lattice of upwardly closed subsets of the original model. We also construct and analyse a 'definable' extension whose points are prime filters of definable sets. A structural explanation is given of why a class that is closed under images of bisimulations and invariant under prime/definable extensions must be invariant under arbitrary ultrapowers. This uses iterated ultrapowers and saturation.
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dc.identifierhttps://doi.org/10.3217/jucs-011-12-1945
dc.identifierhttps://lib.jucs.org/article/28521/
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/8897
dc.languageen
dc.publisherJournal of Universal Computer Science
dc.relationinfo:eu-repo/semantics/altIdentifier/eissn/0948-6968
dc.relationinfo:eu-repo/semantics/altIdentifier/pissn/0948-695X
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightsJ.UCS License
dc.sourceJUCS - Journal of Universal Computer Science 11(12): 1945-1962
dc.subjectintuitionistic logic
dc.subjectKripke model
dc.subjectbisimulation
dc.subjectdisjoint union
dc.subjectprime filter
dc.subjectultraproduct
dc.subjectiterated ultrapower
dc.subjectsaturated model
dc.titleAxiomatic Classes of Intuitionistic Models
dc.typeResearch Article
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