Publications

1. On the lack of colimits in various categories arising in pointfree topology and algebraic logic
   M. Abbadini, G. Bezhanishvili, and L. Carai
   Theory and Applications of Categories 45 (2026), paper no. 20, 759-778
2. Free algebras and coproducts in varieties of Gödel algebras
   L. Carai
   Journal of Symbolic Logic (in press, published online)
3. Duality Theory for Bounded Lattices: A Comparative Study
   G. Bezhanishvili, L. Carai, and P. J. Morandi
   Accepted for publication in Dissertationes Mathematicae
4. Baker-Beynon duality beyond semisimplicity
   L. Carai, S. Lapenta, and L. Spada
   Journal of Algebra 694 (2025), 730-781
5. On the universal theory of the free pseudocomplemented distributive lattice
   L. Carai and T. Moraschini
   Journal of Algebra 682 (2025), 634-671
6. Epimorphisms between finitely generated algebras
   L. Carai, M. Kurtzhals, and T. Moraschini
   Indagationes Mathematicae 36 (2025), no. 5, 1336-1354
7. 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
8. Connecting generalized Priestley duality to Hofmann-Mislove-Stralka duality
   G. Bezhanishvili, L. Carai, and P. J. Morandi
   Theory and Applications of Categories 41 (2024), paper no. 54, 1937-1982
9. 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
10. Vietoris endofunctor for closed relations and its de Vries dual
    M. Abbadini, G. Bezhanishvili, and L. Carai
    Topology Proceedings 64 (2024), 213-250
11. 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
12. 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
13. A frame-theoretic perspective on Esakia duality
    G. Bezhanishvili, L. Carai, and P. J. Morandi
    Algebra universalis 84 (2023), paper no. 30
14. 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
15. 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
16. 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
17. 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
18. 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
19. Temporal interpretation of monadic intuitionistic quantifiers
    G. Bezhanishvili and L. Carai
    Review of Symbolic Logic 16 (2023), no. 1, 164-187
20. Duality for powerset coalgebras
    G. Bezhanishvili, L. Carai, and P. J. Morandi
    Logical Methods in Computer Science 18 (2022), no. 1
21. 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
22. 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
23. Free bounded archimedean ℓ-algebras
    G. Bezhanishvili, L. Carai, and P. J. Morandi
    Applied Categorical Structures 29 (2021), no. 5, 879-888
24. 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
25. Temporal interpretation of intuitionistic quantifiers
    G. Bezhanishvili and L. Carai
    Advances in Modal Logic, vol. 13, College Publications, 2020, pp. 95-114
26. Existentially closed Brouwerian semilattices
    L. Carai and S. Ghilardi
    Journal of Symbolic Logic 84 (2019), no. 4, 1544-1575
27. Characterization of metrizable Esakia spaces via some forbidden configurations
    G. Bezhanishvili and L. Carai
    Algebra universalis 80 (2019), no. 4, paper no. 42

Preprints

32. Ultracontact algebras and stack systems
    L. Carai, I. Düntsch, R. Gruszczyński, A. L. Suarez
33. Implicit operations in varieties of commutative monoids
    L. Carai, M. Kurtzhals, and T. Moraschini
34. The theory of implicit operations
    L. Carai, M. Kurtzhals, and T. Moraschini
35. Esakia's theorem for the amended monadic intuitionistic calculus
    G. Bezhanishvili and L. Carai
36. Failure of Esakia's theorem in the monadic setting
    G. Bezhanishvili and L. Carai

PhD Thesis