A set-theoretic proof of the representation of MV-algebras by sheaves

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Journal of Applied Non-Classical Logics 32 (4):317-334 (2022)
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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.

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2023

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10.1080/11663081.2023.2190007

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Alejandro Estrada
National Autonomous University of Mexico

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Representation theory of MV-algebras.Eduardo J. Dubuc & Yuri A. Poveda - 2010 - Annals of Pure and Applied Logic 161 (8):1024-1046.
Representations of MV-algebras by sheaves.Anna R. Ferraioli & Ada Lettieri - 2011 - Mathematical Logic Quarterly 57 (1):27-43.
MVW-rigs and product MV-algebras.Alejandro Estrada & Yuri A. Poveda - 2018 - Journal of Applied Non-Classical Logics 29 (1):78-96.

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