8 papers
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…
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…
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…
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…
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…
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…