Publications

On the universal theory of the free pseudocomplemented distributive lattice
L. Carai and T. Moraschini
Journal of Algebra 682 (2025), 634-671
Epimorphisms between finitely generated algebras
L. Carai, M. Kurtzhals, and T. Moraschini
Indagationes Mathematicae 36 (2025), no. 5, 1336-1354
A calculus for modal compact Hausdorff spaces
N. Bezhanishvili, L. Carai, S. Ghilardi, and Z. Zhao
Journal of Logic and Computation 35 (2025), no. 6, exae086
Connecting generalized Priestley duality to Hofmann-Mislove-Stralka duality
G. Bezhanishvili, L. Carai, and P. J. Morandi
Theory and Applications of Categories 41 (2024), no. 54, 1937-1982
Failure of the Blok-Esakia Theorem in the monadic setting
G. Bezhanishvili and L. Carai
Annals of Pure and Applied Logic 176 (2025), no. 4, Paper No. 103527
Vietoris endofunctor for closed relations and its de Vries dual
M. Abbadini, G. Bezhanishvili, and L. Carai
Topology Proceedings 64 (2024), 213-250
MacNeille completions of subordination algebras
M. Abbadini, G. Bezhanishvili, and L. Carai
Cahiers de Topologie et Géométrie Différentielle Catégoriques LXV (2024), no. 2, 151-199
A New Proof of the Joyal-Tierney Theorem
G. Bezhanishvili, L. Carai, and P. J. Morandi
Cahiers de Topologie et Géométrie Différentielle Catégoriques LXIV (2023), no. 4, 425-438
A frame-theoretic perspective on Esakia duality
G. Bezhanishvili, L. Carai, and P. J. Morandi
Algebra universalis 84 (2023), no. 30
A generalization of de Vries duality to closed relations between compact Hausdorff spaces
M. Abbadini, G. Bezhanishvili, and L. Carai
Topology and its Applications 337 (2023), Paper No. 108641
A Unified Approach to Gelfand and de Vries Dualities
G. Bezhanishvili, L. Carai, P. J. Morandi, and B. Olberding
Forum Mathematicum 35 (2023), no. 3, 647-676
De Vries powers and proximity Specker algebras
G. Bezhanishvili, L. Carai, P. J. Morandi, and B. Olberding
Applied Categorical Structures 31 (2023), no. 3, Paper No. 24
Admissibility of Π2-Inference Rules: interpolation, model completion, and contact algebras
N. Bezhanishvili, L. Carai, S. Ghilardi, and L. Landi
Annals of Pure and Applied Logic 174 (2023), no. 1, Paper No. 103169
A point-free approach to canonical extensions of boolean algebras and bounded archimedean ℓ-algebras
G. Bezhanishvili, L. Carai, and P. J. Morandi
Order 40 (2023), 257–287
Temporal interpretation of monadic intuitionistic quantifiers
G. Bezhanishvili and L. Carai
Review of Symbolic Logic 16 (2023), no. 1, 164-187
Duality for powerset coalgebras
G. Bezhanishvili, L. Carai, and P. J. Morandi
Logical Methods in Computer Science 18 (2022), no. 1
Modal operators on rings of continuous functions
G. Bezhanishvili, L. Carai, and P. J. Morandi
Journal of Symbolic Logic 87 (2022), no. 4, 1322-1348
The Vietoris functor and modal operators on rings of continuous functions
G. Bezhanishvili, L. Carai, and P. J. Morandi
Annals of Pure and Applied Logic 173 (2022), no. 1, Paper No. 103029
Free bounded archimedean ℓ-algebras
G. Bezhanishvili, L. Carai, and P. J. Morandi
Applied Categorical Structures 29 (2021), no. 5, 879-888
Diego's theorem for nuclear implicative semilattices
G. Bezhanishvili, N. Bezhanishvili, L. Carai, D. Gabelaia, S. Ghilardi, and M. Jibladze
Indagationes Mathematicae (N.S.) 32 (2021), no. 2, 498-535
Temporal interpretation of intuitionistic quantifiers
G. Bezhanishvili and L. Carai
Advances in Modal Logic, vol. 13, College Publications, 2020, pp. 95-114
Existentially closed Brouwerian semilattices
L. Carai and S. Ghilardi
Journal of Symbolic Logic 84 (2019), no. 4, 1544-1575
Characterization of metrizable Esakia spaces via some forbidden configurations
G. Bezhanishvili and L. Carai
Algebra universalis 80 (2019), no. 4, Paper No. 42

Preprints

The theory of implicit operations
L. Carai, M. Kurtzhals, and T. Moraschini
Esakia's theorem for the amended monadic intuitionistic calculus
G. Bezhanishvili and L. Carai
On the lack of colimits in various categories of BAOs and Heyting algebras
M. Abbadini, G. Bezhanishvili, and L. Carai
Duality Theory for Bounded Lattices: A Comparative Study
G. Bezhanishvili, L. Carai, and P. J. Morandi
Failure of Esakia's theorem in the monadic setting
G. Bezhanishvili and L. Carai
Free algebras and coproducts in varieties of Gödel algebras
L. Carai
Baker-Beynon duality beyond semisimplicity
L. Carai, S. Lapenta, and L. Spada

PhD Thesis

New directions in duality theory for modal logic
New Mexico State University, 2021
Supervisor: Prof. G. Bezhanishvili