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  1.  6
    A negative solution of Kuznetsov’s problem for varieties of bi-Heyting algebras.Guram Bezhanishvili, David Gabelaia & Mamuka Jibladze - 2022 - Journal of Mathematical Logic 22 (3).
    Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. In this paper, we show that there exist (continuum many) varieties of bi-Heyting algebras that are not generated by their complete members. It follows that there exist (continuum many) extensions of the Heyting–Brouwer logic [math] that are topologically incomplete. This result provides further insight into the long-standing open problem of Kuznetsov by yielding a negative solution of the reformulation of the problem from extensions of [math] to extensions of [math].
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  2.  24
    An Algebraic Approach to Subframe Logics. Modal Case.Guram Bezhanishvili, Silvio Ghilardi & Mamuka Jibladze - 2011 - Notre Dame Journal of Formal Logic 52 (2):187-202.
    We prove that if a modal formula is refuted on a wK4-algebra ( B ,□), then it is refuted on a finite wK4-algebra which is isomorphic to a subalgebra of a relativization of ( B ,□). As an immediate consequence, we obtain that each subframe and cofinal subframe logic over wK4 has the finite model property. On the one hand, this provides a purely algebraic proof of the results of Fine and Zakharyaschev for K4 . On the other hand, it (...)
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    Scattered toposes.Leo Esakia, Mamuka Jibladze & Dito Pataraia - 2000 - Annals of Pure and Applied Logic 103 (1-3):97-107.
    A class of toposes is introduced and studied, suitable for semantical analysis of an extension of the Heyting predicate calculus admitting Gödel's provability interpretation.
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    Admissible Bases Via Stable Canonical Rules.Nick Bezhanishvili, David Gabelaia, Silvio Ghilardi & Mamuka Jibladze - 2016 - Studia Logica 104 (2):317-341.
    We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics.
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