Publications

  1. Failure of Esakia's theorem in the monadic setting
    G. Bezhanishvili and L. Carai
    Accepted for publication in the Journal of Symbolic Logic
  2. 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
  3. Free algebras and coproducts in varieties of Gödel algebras
    L. Carai
    Journal of Symbolic Logic (in press, published online)
  4. Duality Theory for Bounded Lattices: A Comparative Study
    G. Bezhanishvili, L. Carai, and P. J. Morandi
    Accepted for publication in Dissertationes Mathematicae
  5. Baker-Beynon duality beyond semisimplicity
    L. Carai, S. Lapenta, and L. Spada
    Journal of Algebra 694 (2025), 730-781
  6. On the universal theory of the free pseudocomplemented distributive lattice
    L. Carai and T. Moraschini
    Journal of Algebra 682 (2025), 634-671
  7. Epimorphisms between finitely generated algebras
    L. Carai, M. Kurtzhals, and T. Moraschini
    Indagationes Mathematicae 36 (2025), no. 5, 1336-1354
  8. 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
  9. 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
  10. 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
  11. Vietoris endofunctor for closed relations and its de Vries dual
    M. Abbadini, G. Bezhanishvili, and L. Carai
    Topology Proceedings 64 (2024), 213-250
  12. 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
  13. 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
  14. A frame-theoretic perspective on Esakia duality
    G. Bezhanishvili, L. Carai, and P. J. Morandi
    Algebra universalis 84 (2023), paper no. 30
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. Temporal interpretation of monadic intuitionistic quantifiers
    G. Bezhanishvili and L. Carai
    Review of Symbolic Logic 16 (2023), no. 1, 164-187
  21. Duality for powerset coalgebras
    G. Bezhanishvili, L. Carai, and P. J. Morandi
    Logical Methods in Computer Science 18 (2022), no. 1
  22. 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
  23. 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
  24. Free bounded archimedean ℓ-algebras
    G. Bezhanishvili, L. Carai, and P. J. Morandi
    Applied Categorical Structures 29 (2021), no. 5, 879-888
  25. 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
  26. Temporal interpretation of intuitionistic quantifiers
    G. Bezhanishvili and L. Carai
    Advances in Modal Logic, vol. 13, College Publications, 2020, pp. 95-114
  27. Existentially closed Brouwerian semilattices
    L. Carai and S. Ghilardi
    Journal of Symbolic Logic 84 (2019), no. 4, 1544-1575
  28. Characterization of metrizable Esakia spaces via some forbidden configurations
    G. Bezhanishvili and L. Carai
    Algebra universalis 80 (2019), no. 4, paper no. 42

Preprints

  1. A completion of reduced commutative rings
    L. Carai, M. Kurtzhals, and T. Moraschini
  2. Ultracontact algebras and stack systems
    L. Carai, I. Düntsch, R. Gruszczyński, A. L. Suarez
  3. Implicit operations in varieties of commutative monoids
    L. Carai, M. Kurtzhals, and T. Moraschini
  4. The theory of implicit operations
    L. Carai, M. Kurtzhals, and T. Moraschini
  5. Esakia's theorem for the amended monadic intuitionistic calculus
    G. Bezhanishvili and L. Carai

PhD Thesis

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

Notes