3 citations · 19 across the 44 of their papers we have counts for
54 papers
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…
The Funayama envelope as the -hull of a frame
Guram Bezhanishvili, Ranjitha Raviprakash, Anna Laura Suarez +1
We introduce proximity morphisms between MT-algebras and show that the resulting category is equivalent to the category of frames. This is done by utilizing the Funayama envelope o…
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…
The category of topological spaces and open maps does not have products
Guram Bezhanishvili, Andre Kornell
We prove that the category of topological spaces and open maps does not have binary products, thus resolving the Esakia problem in the negative. We also prove that the categories o…
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…
Subfitness in distributive (semi)lattices
Guram Bezhanishvili, James Madden, M. Andrew Moshier +2
We investigate whether the set of subfit elements of a distributive semilattice is an ideal. This question was raised by the second author at the BLAST conference in 2022. We show…
Local compactness in MT-algebras
Guram Bezhanishvili, Ranjitha Raviprakash
In our previous work, we introduced McKinsey-Tarski algebras (MT-algebras for short) as an alternative pointfree approach to topology. Here we study local compactness in MT-algebra…
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…
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…
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^{…
McKinsey-Tarski Algebras: An alternative pointfree approach to topology
Guram Bezhanishvili, Ranjitha Raviprakash
McKinsey and Tarski initiated the study of interior algebras. We propose complete interior algebras as an alternative pointfree approach to topology. We term these algebras McKinse…
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…
Deriving dualities in pointfree topology from Priestley duality
G. Bezhanishvili, S. Melzer
There are several prominent duality results in pointfree topology. The Hofmann-Lawson duality establishes that the category of continuous frames is dually equivalent to the categor…
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…
Remarks on Hyperspaces for Priestley Spaces
G. Bezhanishvili, J. Harding, P. J. Morandi
The Vietoris space of a Stone space plays an important role in the coalgebraic approach to modal logic. When generalizing this to positive modal logic, there is a variety of releva…