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  1.  23
    Admissibility of Π2-Inference Rules: interpolation, model completion, and contact algebras.Nick Bezhanishvili, Luca Carai, Silvio Ghilardi & Lucia Landi - 2023 - Annals of Pure and Applied Logic 174 (1):103169.
  2.  10
    Modal Operators on Rings of Continuous Functions.Guram Bezhanishvili, Luca Carai & Patrick J. Morandi - 2022 - Journal of Symbolic Logic 87 (4):1322-1348.
    It is a classic result in modal logic, often referred to as Jónsson-Tarski duality, that the category of modal algebras is dually equivalent to the category of descriptive frames. The latter are Kripke frames equipped with a Stone topology such that the binary relation is continuous. This duality generalizes the celebrated Stone duality for boolean algebras. Our goal is to generalize descriptive frames so that the topology is an arbitrary compact Hausdorff topology. For this, instead of working with the boolean (...)
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  3.  16
    Temporal Interpretation of Monadic Intuitionistic Quantifiers.Guram Bezhanishvili & Luca Carai - 2023 - Review of Symbolic Logic 16 (1):164-187.
    We show that monadic intuitionistic quantifiers admit the following temporal interpretation: “always in the future” (for$\forall $) and “sometime in the past” (for$\exists $). It is well known that Prior’s intuitionistic modal logic${\sf MIPC}$axiomatizes the monadic fragment of the intuitionistic predicate logic, and that${\sf MIPC}$is translated fully and faithfully into the monadic fragment${\sf MS4}$of the predicate${\sf S4}$via the Gödel translation. To realize the temporal interpretation mentioned above, we introduce a new tense extension${\sf TS4}$of${\sf S4}$and provide a full and faithful translation (...)
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  4.  11
    Existentially closed Brouwerian semilattices.Luca Carai & Silvio Ghilardi - 2019 - Journal of Symbolic Logic 84 (4):1544-1575.
    The variety of Brouwerian semilattices is amalgamable and locally finite; hence, by well-known results [19], it has a model completion. In this article, we supply a finite and rather simple axiomatization of the model completion.
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  5.  6
    New Directions in Duality Theory for Modal Logic.Luca Carai - 2021 - Bulletin of Symbolic Logic 27 (4):527-527.
    In this work we present some new contributions towards two different directions in the study of modal logic. First we employ tense logics to provide a temporal interpretation of intuitionistic quantifiers as “always in the future” and “sometime in the past.” This is achieved by modifying the Gödel translation and resolves an asymmetry between the standard interpretation of intuitionistic quantifiers.Then we generalize the classic Gelfand–Naimark–Stone duality between compact Hausdorff spaces and uniformly complete bounded archimedean $\ell $ -algebras to a duality (...)
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