Abelian \(\ell\)-groups with strong unit and perfect MV-algebras
type: Item
instance of: scholarly article
title: Abelian \(\ell\)-groups with strong unit and perfect MV-algebras
zbMATH Open document ID: 1168.06006
author: Brunella Gerla
author: Peter L. Belluce
author: Antonio Di Nola
published in: Order
publication date: 2009-04-24T00:00:00Z
review text: In his paper [J. Funct. Anal. 65, 15--63 (1986; Zbl 0597.46059)], the present reviewer established a categorical equivalence \(\Gamma\) between MV-algebras and unital lattice-ordered abelian groups. MV-algebras stand to Boolean algebras as infinite-valued Łukasiewicz logic stands to Boolean logic. They were introduced in 1958 by C. C. Chang to prove the completeness theorem for Łukasiewicz infinite-valued propositional logic. By definition, perfect MV-algebras are generated by their radical. They were more recently introduced by Belluce, Di Nola and B. Gerla, and shown to be categorically equivalent to lattice-ordered abelian groups. In the present paper, the authors describe the \(\Gamma\)-correspondents of perfect MV-algebras and of local MV-algebras with finite rank.
reviewed by: Daniele Mundici
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 03B50
zbMATH DE Number: 5547257
zbMATH Keywords: order-unit
zbMATH Keywords: perfect MV-algebras
zbMATH Keywords: lattice-ordered abelian groups
zbMATH Keywords: local MV-algebras
MaRDI profile type: Publication
full work available at URL: s11083-008-9103-7
OpenAlex ID: W1974524636
cites work: Perfect MV-algebras and their logic
cites work: Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory
cites work: The going up and going down theorems in MV-algebras and abelian \(l\)-groups
cites work: A weak completeness theorem for infinite valued first-order logic
cites work: Q4680302
cites work: Algebraic Analysis of Many Valued Logics
cites work: Algebraic foundations of many-valued reasoning
cites work: Q4317872
cites work: Local algebras in the representation of MV-algebras
cites work: Representation and reticulation by quotients of MV-algebras
cites work: Perfect MV-algebras are categorically equivalent to Abelian \(l\)-groups
cites work: Equational characterization of all varieties of MV-algebras
cites work: Strong non-standard completeness for fuzzy logics
cites work: Uniformly hyperarchimedean lattice-ordered groups
cites work: Super-Łukasiewicz propositional logics
cites work: Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
cites work: Die nichtaxiomatisierbarkeit des unendlichwertigen Prädikatenkalküls von Łukasiewicz
cites work: Cyclic Elements in MV‐Algebras and Post Algebras
DOI: 10.1007/S11083-008-9103-7
description: scientific article; zbMATH DE number 5547257