A duality for (n+1)-valued MV-algebras

TL;DR

This paper establishes a categorical equivalence between (n+1)-valued MV-algebras and Boolean algebras with specific filters, connecting existing dualities and duality theories in MV-algebra research.

Contribution

It introduces a new categorical equivalence linking (n+1)-valued MV-algebras to Boolean algebras with filters, expanding the understanding of their structural relationships.

Findings

Categorical equivalence between (n+1)-valued MV-algebras and Boolean algebras with filters

Connections between this equivalence and existing dualities in MV-algebra theory

Relations to duality results by Cignoli and Niederkorn

Abstract

MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Lukasiewicz propositional calculus. In this paper we give a categorical equivalence between the varieties of (n+1)-valued MV-algebras and the classes of Boolean algebras endowed with a certain family of filters. Another similar categorical equivalence is given by A. Di Nola and A. Lettieri. Also, we point out the relations between this categorical equivalence and the duality established by R. Cignoli, which can be derived from results obtained by P. Niederkorn on natural dualities for varieties of MV-algebras.