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Abstract: In this paper we develop a general representation theory for mv-algebras. Wefurnish the appropriate categorical background to study this problem. Our guideline is the theory of classifying topoi of coherent extensions of universalalgebra theories. Our main result corresponds, in the case of mv-algebras andmv-chains, to the representation of commutative rings with unit as rings ofglobal sections of sheaves of local rings. \emph{We prove that any mv-algebrais isomorphic to the mv-algebra of all global sections of a sheaf of mv-chainson a compact topological space}. This result is intimately related toMcNaughton-s theorem, and we explain why our representation theorem can beviewed as a vast generalization of McNaughton-s. On spite of the languageutilized in this abstract, we wrote this paper in a way that, we hope, could beread without much acquaintance with either sheaf theory or mv-algebra theory.



Author: Eduardo J. Dubuc, Yuri A. Poveda

Source: https://arxiv.org/







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