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

A set-theoretic proof of the representation of MV-algebras by sheaves 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

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

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Publisher
Taylor & Francis
Copyright
© 2023 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.2023.2190007
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Applied Non-Classical Logics – Taylor & Francis

Published: Oct 2, 2022

Keywords: MV-algebra; spectrum; sheaf; representation; 06D35; 06D05; 06D50; 06D22

References

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