\(\mu \)MV-algebras: An approach to fixed points in Łukasiewicz logic
type: Item
instance of: scholarly article
title: \(\mu \)MV-algebras: An approach to fixed points in Łukasiewicz logic
zbMATH Open document ID: 1183.06006
author: Luca Spada
published in: Fuzzy Sets and Systems
publication date: 2009-08-28T00:00:00Z
review text: Chang introduced MV-algebras to give a purely algebraic proof of the completeness of the Łukasiewicz axioms. In his paper [J. Funct. Anal. 65, 15--63 (1986; Zbl 0597.46059)], the present reviewer established a categorical equivalence between MV-algebras and unital lattice-ordered abelian groups. Divisible MV-algebras are the correspondents of divisible unital lattice-ordered abelian groups. By further equipping a divisible MV-algebra with the well-known \(\Delta\)-operator, one has divisible MV\(_\Delta\)-algebras. The author proves that by expanding MV-algebras to structures allowing minimal and maximal fixed points, one obtains a term-equivalent variant of divisible MV\(_\Delta\)-algebras. He then derives various kinds of results on these algebras, such as subdirect representation, completeness, amalgamation and a representation of free algebras. For background on MV-algebras see the monograph [\textit{R. L. O. Cignoli, I. M. L. D'Ottaviano} and \textit{D. Mundici}, Algebraic foundations of many-valued reasoning. Dordrecht: Kluwer Academic Publishers (2000; Zbl 0937.06009)].
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03G25
zbMATH DE Number: 5599399
zbMATH Keywords: MV-algebra
zbMATH Keywords: lattice-ordered group
zbMATH Keywords: many-valued logic
zbMATH Keywords: divisible MV-algebra
zbMATH Keywords: \(\Delta\)-operator
zbMATH Keywords: fixed point
reviewed by: Daniele Mundici
MaRDI profile type: Publication
full work available at URL: j.fss.2007.12.010
OpenAlex ID: W1985651708
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DOI: 10.1016/J.FSS.2007.12.010
description: scientific article; zbMATH DE number 5599399