3 citations · 19 across the 44 of their papers we have counts for
26 papers · 1 filter
Esakia order-compactifications and locally Esakia spaces
Rodrigo Nicolau Almeida, Guram Bezhanishvili, Nick Bezhanishvili
We introduce Esakia order-compactifications and study how they fit in the general theory of Priestley order-compactifications. We provide an analog of Dwinger's theorem by characte…
Finite axiomatization of and
Guram Bezhanishvili, Mashiath Khan
We prove that is product matching, and that is axiomatizable by adding to the Gödel…
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…
Maximality Principles in Modal Logic and the Axiom of Choice
Rodrigo Nicolau Almeida, Guram Bezhanishvili
We investigate the set-theoretic strength of several maximality principles that play an important role in the study of modal and intuitionistic logics. We focus on the well-known F…
The Monadic Grzegorczyk Logic
Guram Bezhanishvili, Mashiath Khan
We develop a semantic criterion for determining whether a given monadic modal logic axiomatizes the one-variable fragment of a predicate modal logic. We show that the criterion app…
Duality for distributive and implicative semi-lattices
Guram Bezhanishvili, Ramon Jansana
We develop a new duality for distributive and implicative meet semi-lattices. For distributive meet semi-lattices our duality generalizes Priestley's duality for distributive latti…
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…
Local finiteness in varieties of MS4-algebras
Guram Bezhanishvili, Chase Meadors
It is a classic result of Segerberg and Maksimova that a variety of -algebras is locally finite iff it is of finite depth. Since the logic (monadic $\ma…
On Shehtman's Two Problems
Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan +1
We provide partial solutions to two problems posed by Shehtman concerning the modal logic of the Čech-Stone compactification of an ordinal space. We use the Continuum Hypothesis to…
On the structure of modal and tense operators on a boolean algebra
Guram Bezhanishvili, Andre Kornell
We study the poset NO(B) of necessity operators on a boolean algebra B. We show that NO(B) is a meet-semilattice that need not be distributive. However, when B is complete, NO(B) i…
Degrees of the finite model property: the antidichotomy theorem
Guram Bezhanishvili, Nick Bezhanishvili, Tommaso Moraschini
A classic result in modal logic, known as the Blok Dichotomy Theorem, states that the degree of incompleteness of a normal extension of the basic modal logic is or $2^{…
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…
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…
Hofmann-Mislove through the Lenses of Priestley
G. Bezhanishvili, S. Melzer
We use Priestley duality to give a new proof of the Hofmann-Mislove Theorem.
Epimorphisms in varieties of residuated structures
G. Bezhanishvili, T. Moraschini, J. Raftery
It is proved that epimorphisms are surjective in a range of varieties of residuated structures, including all varieties of Heyting or Brouwerian algebras of finite depth, and all v…
A negative solution of Kuznetsov's problem for varieties of bi-Heyting algebras
Guram Bezhanishvili, David Gabelaia, Mamuka Jibladze
We show that there exist (continuum many) varieties of bi-Heyting algebras that are not generated by their complete members. It follows that there exist (continuum many) extensions…
Monadic Intuitionistic and Modal Logics Admitting Provability Interpretations
Guram Bezhanishvili, Kristina Brantley, Julia Ilin
The Gödel translation provides an embedding of the intuitionistic logic into the modal logic , which then embeds into the modal logic via…
Profiniteness and representability of spectra of Heyting algebras
G. Bezhanishvili, N. Bezhanishvili, T. Moraschini +1
We prove that there exist profinite Heyting algebras that are not isomorphic to the profinite completion of any Heyting algebra. This resolves an open problem from 2009. More gener…
The Baire closure and its logic
Guram Bezhanishvili, David Fernández-Duque
The Baire algebra of a topological space is the quotient of the algebra of all subsets of modulo the meager sets. We show that this Boolean algebra can be endowed with a na…
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…
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…