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

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.

KEYWORDS:

• MV-algebra
• spectrum
• sheaf
• representation

AMS SUBJECT CLASSIFICATIONS:

• 06D35
• 06D05
• 06D50
• 06D22

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

A. Estrada was partially supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) [Finance Code 001].