Publications

A calculus for modal compact Hausdorff spaces
N. Bezhanishvili, L. Carai, S. Ghilardi, and Z. Zhao
Accepted for publication in the Journal of Logic and Computation
Connecting generalized Priestley duality to Hofmann-Mislove-Stralka duality
G. Bezhanishvili, L. Carai, and P. J. Morandi
Theory Appl. Categ. 41 (2024), no. 54, 1937-1982
Failure of the Blok-Esakia Theorem in the monadic setting
G. Bezhanishvili and L. Carai
Ann. Pure Appl. Log. 176 (2025), no. 4, Paper No. 103527
Vietoris endofunctor for closed relations and its de Vries dual
M. Abbadini, G. Bezhanishvili, and L. Carai
Top. Proc. 64 (2024), 213-250
MacNeille completions of subordination algebras
M. Abbadini, G. Bezhanishvili, and L. Carai
Cah. Topol. Géom. Différ. Catég. 65 (2024), no. 2, 151-199
A New Proof of the Joyal-Tierney Theorem
G. Bezhanishvili, L. Carai, and P. J. Morandi
Cah. Topol. Géom. Différ. Catég. LXIV (2023), no. 4, 425-438
A frame-theoretic perspective on Esakia duality
G. Bezhanishvili, L. Carai, and P. J. Morandi
Algebra Univers. 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 Appl. 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 Math. 35 (2023), no. 3, 647-676
De Vries powers and proximity Specker algebras
G. Bezhanishvili, L. Carai, P. J. Morandi, and B. Olberding
Appl. Categ. 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
Ann. Pure Appl. Log. 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
Rev. Symb. Log. 16 (2023), no. 1, 164-187
Duality for powerset coalgebras
G. Bezhanishvili, L. Carai, and P. J. Morandi
Log. Methods Comput. Sci. 18 (2022), no. 1
Modal operators on rings of continuous functions
G. Bezhanishvili, L. Carai, and P. J. Morandi
J. Symb. Log. 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
Ann. Pure Appl. Log. 173 (2022), no. 1, Paper No. 103029
Free bounded archimedean ℓ-algebras
G. Bezhanishvili, L. Carai, and P. J. Morandi
Appl. Categ. Struct. 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
Indag. Math. (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
J. Symb. Log. 84 (2019), no. 4, 1544-1575
Characterization of metrizable Esakia spaces via some forbidden configurations
G. Bezhanishvili and L. Carai
Algebra Univers. 80 (2019), no. 4, Paper No. 42

Submitted preprints

Failure of Esakia's theorem in the monadic setting
G. Bezhanishvili and L. Carai
On the universal theory of the free pseudocomplemented distributive lattice
L. Carai and T. Moraschini
Free algebras and coproducts in varieties of Gödel algebras
L. Carai
Epimorphisms between finitely generated algebras
L. Carai, M. Kurtzhals, and T. Moraschini
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