3 citations · 7 across the 18 of their papers we have counts for
23 papers
Esakia's theorem for the amended monadic intuitionistic calculus
Guram Bezhanishvili, Luca Carai
We show that the amended monadic Grzegorczyk logic is the largest modal companion of the amended monadic intuitionistic logic . Thus, unlike the…
On the lack of colimits in various categories arising in pointfree topology and algebraic logic
Marco Abbadini, Guram Bezhanishvili, Luca Carai
We prove that the category of McKinsey-Tarski algebras is not equivalent to a variety of algebras, thus answering a question of Peter Jipsen in the negative. More generally, we sho…
Duality Theory for Bounded Lattices: A Comparative Study
Guram Bezhanishvili, Luca Carai, Patrick Morandi
There are numerous generalizations of the celebrated Priestley duality for bounded distributive lattices to the non-distributive setting. The resulting dualities rely on an earlier…
Failure of Esakia's theorem in the monadic setting
Guram Bezhanishvili, Luca Carai
Esakia's theorem states that Grzegorczyk's logic is the greatest modal companion of intuitionistic propositional calculus. We prove that already the one-variable fragment of intuit…
Failure of the Blok-Esakia Theorem in the monadic setting
Guram Bezhanishvili, Luca Carai
The Blok-Esakia Theorem establishes that the lattice of superintuitionistic logics is isomorphic to the lattice of extensions of Grzegorczyk's logic. We prove that the Blok-Esakia…
A calculus for modal compact Hausdorff spaces
Nick Bezhanishvili, Luca Carai, Silvio Ghilardi +1
The symmetric strict implication calculus is a modal calculus for compact Hausdorff spaces. This is established through de Vries duality, linking compact Hausdorff…
Vietoris endofunctor for closed relations and its de Vries dual
Marco Abbadini, Guram Bezhanishvili, Luca Carai
We generalize the classic Vietoris endofunctor to the category of compact Hausdorff spaces and closed relations. The lift of a closed relation is done by generalizing the construct…
A New Proof of the Joyal-Tierney Theorem
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We give an alternative, more geometric, proof of the well-known Joyal-Tierney Theorem in locale theory by utilizing Priestley duality for frames.
Heyting frames and Esakia duality
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We introduce the category of Heyting frames and show that it is equivalent to the category of Heyting algebras and dually equivalent to the category of Esakia spaces. This provides…
MacNeille completions of subordination algebras
Marco Abbadini, Guram Bezhanishvili, Luca Carai
-subordination algebras are a natural generalization of de Vries algebras. Recently it was proved that the category of -subordination a…
Connecting generalized Priestley duality to Hofmann-Mislove-Stralka duality
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other thi…
A generalization of de Vries duality to closed relations between compact Hausdorff spaces
Marco Abbadini, Guram Bezhanishvili, Luca Carai
Stone duality generalizes to an equivalence between the categories of Stone spaces and closed relations and of boolean algebr…
A Unified Approach to Gelfand and de Vries Dualities
Guram Bezhanishvili, Luca Carai, Patrick Morandi +1
We develop a unified approach to Gelfand and de Vries dualities for compact Hausdorff spaces, which is based on appropriate modifications of the classic results of Dieudonné (analy…
Admissibility of -Inference Rules: interpolation, model completion, and contact algebras
Nick Bezhanishvili, Luca Carai, Silvio Ghilardi +1
We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to…
De Vries powers and proximity Specker algebras
G. Bezhanishvili, L. Carai, P. Morandi +1
By de Vries duality [9], the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras. In [5] an alternate duality f…
Temporal interpretation of intuitionistic quantifiers: Monadic case
Guram Bezhanishvili, Luca Carai
In a recent paper we showed that intuitionistic quantifiers admit the following temporal interpretation: "always in the future" (for ) and "sometime in the past" (for $\ex…
Temporal interpretation of intuitionistic quantifiers
Guram Bezhanishvili, Luca Carai
We show that intuitionistic quantifiers admit the following temporal interpretation: is true at a world iff is true at every object in the domain of every fut…
Characterization of metrizable Esakia spaces via some forbidden configurations
Guram Bezhanishvili, Luca Carai
By Priestley duality, each bounded distributive lattice is represented as the lattice of clopen upsets of a Priestley space, and by Esakia duality, each Heyting algebra is represen…
Free bounded archimedean -algebras
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We show that free objects on sets do not exist in the category of bounded archimedean -algebras. On the other hand, we introduce the category of weighted sets and prove…
Duality for powerset coalgebras
Guram Bezhanishvili, Luca Carai, Patrick Morandi
Let CABA be the category of complete and atomic boolean algebras and complete boolean homomorphisms, and let CSL be the category of complete meet-semilattices and complete meet-hom…
Diego's Theorem for nuclear implicative semilattices
Guram Bezhanishvili, Nick Bezhanishvili, Luca Carai +3
We prove that the variety of nuclear implicative semilattices is locally finite, thus generalizing Diego's Theorem. The key ingredients of our proof include the coloring technique…
Modal operators on rings of continuous functions
Guram Bezhanishvili, Luca Carai, Patrick Morandi
It is a classic result in modal logic that the category of modal algebras is dually equivalent to the category of descriptive frames. The latter are Kripke frames equipped with a S…
Existentially Closed Brouwerian Semilattices
Luca Carai, Silvio Ghilardi
The variety of Brouwerian semilattices is amalgamable and locally finite, hence by well-known results due to W. H. Wheeler, it has a model completion (whose models are the existent…