Profinite MV-algebras

TL;DR

This paper characterizes profinite MV-algebras as direct products of finite chains, establishes a duality with the category of multisets, and generalizes known results from finite MV-algebras.

Contribution

It provides a complete characterization of profinite MV-algebras and establishes a duality with multisets, extending finite MV-algebra results to the profinite case.

Findings

Profinite MV-algebras are exactly direct products of finite Łukasiewicz chains.

The category of multisets is dually equivalent to a category of profinite MV-algebras.

Generalization of finite MV-algebra duality to profinite MV-algebras.

Abstract

We characterize all profinite MV-algebras, these are MV-algebras that are inverse limits of finite MV-algebras. It is shown that these are exactly direct product of finite \L ukasiewicz's chains. We also prove that the category $\mathbb{M}$ of multisets is dually equivalent to the category $\mathbb{P}$ of profinite MV-algebras and homomorphisms that reflect principal maximal ideals. Thus generalizing the corresponding result for finite MV-algebras, and finite multisets.