A set-theoretic proof of the representation of MV-algebras by sheaves. Issue 4 (2nd October 2022)

• Record Type: Journal Article
• Authors: Estrada, Alejandro; Poveda, Yuri A.
• Is Part Of: Journal of applied non-classical logics. Volume 32:Issue 4(2022)
• Page Start: 317
• Page End: 334
• Publication Date: 2022-10-02
• Subjects: MV-algebra -- spectrum -- sheaf -- representation; 06D35 -- 06D05 -- 06D50 -- 06D22; Nonclassical mathematical logic -- Periodicals; Wiskundige logica; Logic; Periodicals; 511.3105
• DOI: 10.1080/11663081.2023.2190007
• Languages: English
• ISSNs: 1166-3081

Abstract

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.