9 found
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  1.  35
    On monadic MV-algebras.Antonio Di Nola & Revaz Grigolia - 2004 - Annals of Pure and Applied Logic 128 (1-3):125-139.
    We define and study monadic MV-algebras as pairs of MV-algebras one of which is a special case of relatively complete subalgebra named m-relatively complete. An m-relatively complete subalgebra determines a unique monadic operator. A necessary and sufficient condition is given for a subalgebra to be m-relatively complete. A description of the free cyclic monadic MV-algebra is also given.
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  2.  61
    Nonsense logics and their algebraic properties.Victor K. Finn & Revaz Grigolia - 1993 - Theoria 59 (1-3):207-273.
  3.  32
    Representations of monadic MV -algebras.L. Peter Belluce, Revaz Grigolia & Ada Lettieri - 2005 - Studia Logica 81 (1):123-144.
    Representations of monadic MV -algebra, the characterization of locally finite monadic MV -algebras, with axiomatization of them, definability of non-trivial monadic operators on finitely generated free MV -algebras are given. Moreover, it is shown that finitely generated m-relatively complete subalgebra of finitely generated free MV -algebra is projective.
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  4.  49
    Finitely generated free MV-algebras and their automorphism groups.Antonio Di Nola, Revaz Grigolia & Giovanni Panti - 1998 - Studia Logica 61 (1):65-78.
    The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...)
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  5.  15
    Gödel spaces and perfect MV-algebras.Antonio Di Nola & Revaz Grigolia - 2015 - Journal of Applied Logic 13 (3):270-284.
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  6.  16
    Formulas of one propositional variable in intuitionistic logic with the Solovay modality.Leo Esakia & Revaz Grigolia - 2008 - Logic and Logical Philosophy 17 (1-2):111-127.
    A description of the free cyclic algebra over the variety of Solovay algebras, as well as over its pyramid locally finite subvarieties is given.
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  7.  48
    A discrete representation of free MV-algebras.Antonio Di Nola, Revaz Grigolia & Luca Spada - 2010 - Mathematical Logic Quarterly 56 (3):279-288.
    We prove that the m -generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the m -generated free MV-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV-algebras and special maps between them as morphisms.
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  8.  20
    Critical varieties of bi-closure algebras.Revaz Grigolia & Slava Meskhi - 1981 - Bulletin of the Section of Logic 10 (1):2-6.
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  9.  22
    Free and Projective Bimodal Symmetric Gödel Algebras.Revaz Grigolia, Tatiana Kiseliova & Vladimer Odisharia - 2016 - Studia Logica 104 (1):115-143.
    Gödel logic is the extension of intuitionistic logic by the linearity axiom. Symmetric Gödel logic is a logical system, the language of which is an enrichment of the language of Gödel logic with their dual logical connectives. Symmetric Gödel logic is the extension of symmetric intuitionistic logic. The proof-intuitionistic calculus, the language of which is an enrichment of the language of intuitionistic logic by modal operator was investigated by Kuznetsov and Muravitsky. Bimodal symmetric Gödel logic is a logical system, the (...)
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