Profinite completions and MacNeille completions of MV-algebras

TL;DR

This paper characterizes the profinite and MacNeille completions of MV-algebras, generalizing known results from Boolean algebras and identifying conditions for their isomorphism.

Contribution

It provides a comprehensive description of profinite completions of MV-algebras and characterizes when these are isomorphic to MacNeille completions.

Findings

Profinite completions of MV-algebras generalize Boolean algebra cases.

Characterization of profinite MV-algebras as completions.

Conditions under which profinite and MacNeille completions are isomorphic.

Abstract

We determine the profinite completions of MV-algebras, and obtain a description that generalizes the well known profinite completions of Boolean algebras as the power sets of their Stone spaces. We also use the description found to characterize profinite MV-algebras that are isomorphic to the profinite completion of an MV-algebra. Finally, MV-algebras for which the profinite Completion and MacNeille completion are isomorphic are characterized.