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  1. Algebraically closed MV-algebras and their sheaf representation.Antonio Di Nola, Anna R. Ferraioli & Giacomo Lenzi - 2013 - Annals of Pure and Applied Logic 164 (3):349-355.
    In this paper we first provide a new axiomatization of algebraically closed MV-algebras based on McNaughtonʼs Theorem. Then we turn to sheaves, and we represent algebraically closed MV-algebras as algebras of global sections of sheaves, where the stalks are divisible MV-chains and the base space is Stonean.
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  • A set-theoretic proof of the representation of MV-algebras by sheaves.Alejandro Estrada & Yuri A. Poveda - 2022 - Journal of Applied Non-Classical Logics 32 (4):317-334.
    In this paper, we provide a set-theoretic proof of the general representation theorem for MV-algebras, which was developed by Dubuc and Poveda in 2010. The theorem states that every MV-algebra is isomorphic to the MV-algebra of all global sections of its prime spectrum. We avoid using topos theory and instead rely on basic concepts from MV-algebras, topology and set theory.
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  • The Intimate Relationship Between the McNaughton and the Chinese Remainder Theorems for MV-algebras.Eduardo J. Dubuc & Yuri Poveda - 2013 - Studia Logica 101 (3):483-485.
    We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include a simple proof of this theorem inspired in Ferraioli (...)
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