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A set-theoretic proof of the representation of MV-algebras by sheaves
Journal of Applied Non-Classical Logics 32 (4):317-334 (2022)
Abstract
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.Author's Profile
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References found in this work
Algebraic foundations of many-valued reasoning.Roberto Cignoli - 1999 - Boston: Kluwer Academic Publishers. Edited by Itala M. L. D'Ottaviano & Daniele Mundici.
Representation theory of MV-algebras.Eduardo J. Dubuc & Yuri A. Poveda - 2010 - Annals of Pure and Applied Logic 161 (8):1024-1046.
Erratum to “Representation theory of MV-algebras” [Ann. Pure Appl. Logic 161 (8) (2010)].Eduardo J. Dubuc - 2012 - Annals of Pure and Applied Logic 163 (9):1358.
On the Equivalence Between MV-Algebras and l-Groups with Strong Unit.Eduardo J. Dubuc & Y. A. Poveda - 2015 - Studia Logica 103 (4):807-814.
Representations of MV-algebras by sheaves.Anna R. Ferraioli & Ada Lettieri - 2011 - Mathematical Logic Quarterly 57 (1):27-43.
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