Switch to: References

Add citations

You must login to add citations.
  1. An algebraic approach to subframe logics. Intuitionistic case.Guram Bezhanishvili & Silvio Ghilardi - 2007 - Annals of Pure and Applied Logic 147 (1):84-100.
    We develop duality between nuclei on Heyting algebras and certain binary relations on Heyting spaces. We show that these binary relations are in 1–1 correspondence with subframes of Heyting spaces. We introduce the notions of nuclear and dense nuclear varieties of Heyting algebras, and prove that a variety of Heyting algebras is nuclear iff it is a subframe variety, and that it is dense nuclear iff it is a cofinal subframe variety. We give an alternative proof that every subframe variety (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • An Algebraic Approach to Canonical Formulas: Modal Case.Guram Bezhanishvili & Nick Bezhanishvili - 2011 - Studia Logica 99 (1-3):93-125.
    We introduce relativized modal algebra homomorphisms and show that the category of modal algebras and relativized modal algebra homomorphisms is dually equivalent to the category of modal spaces and partial continuous p-morphisms, thus extending the standard duality between the category of modal algebras and modal algebra homomorphisms and the category of modal spaces and continuous p-morphisms. In the transitive case, this yields an algebraic characterization of Zakharyaschev’s subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Should Anti-Realists be Anti-Realists About Anti-Realism?Roy T. Cook - 2014 - Erkenntnis 79 (S2):233-258.
    On the Dummettian understanding, anti-realism regarding a particular discourse amounts to (or at the very least, involves) a refusal to accept the determinacy of the subject matter of that discourse and a corresponding refusal to assert at least some instances of excluded middle (which can be understood as expressing this determinacy of subject matter). In short: one is an anti-realist about a discourse if and only if one accepts intuitionistic logic as correct for that discourse. On careful examination, the strongest (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Not Every Splitting Heyting or Interior Algebra is Finitely Presentable.Alex Citkin - 2012 - Studia Logica 100 (1-2):115-135.
    We give an example of a variety of Heyting algebras and of a splitting algebra in this variety that is not finitely presentable. Moreover, we show that the corresponding splitting pair cannot be defined by any finitely presentable algebra. Also, using the Gödel-McKinsey-Tarski translation and the Blok-Esakia theorem, we construct a variety of Grzegorczyk algebras with similar properties.
    Download  
     
    Export citation  
     
    Bookmark   1 citation