The variety generated by perfect BL-algebras: an algebraic approach in a fuzzy logic setting
type: Item
instance of: scholarly article
title: The variety generated by perfect BL-algebras: an algebraic approach in a fuzzy logic setting
zbMATH Open document ID: 1004.03023
DOI: 10.1023/A:1014539401842
author: Antonio Di Nola
author: Salvatore Sessa
author: Francesc Esteva
author: Lluís Godo
author: Pere García
published in: Annals of Mathematics and Artificial Intelligence
publication date: 2002-06-27T00:00:00Z
review text: BL-algebras are the algebras of Hajek's Basic Logic [see \textit{P. Hájek}, Metamathematics of fuzzy logic. Trends in Logic, Studia Logica Library. 4. Dordrecht: Kluwer Academic Publishers (1998; Zbl 0937.03030)]. In the absence of a notion of ideal, the spectral theory of BL-algebras can be investigated using filters -- the latter being the algebraic counterpart of deductive systems. The main results of this paper deal with the variety generated by ``perfect'' BL-algebras, and the class of ``bipartite'' BL-algebras, generalizing previous results on perfect and bipartite MV-algebras. Warning: the authors' usage of the terminology ``locally finite'' (which in the particular case of MV-algebras boils down to ``without homomorphic images'') does not conform to current usage in universal algebra (where \(A\) is ``locally finite'' iff every finitely generated subalgebra of \(A\) is finite). This may lead to confusion: For instance, there exist singly generated infinite MV-subalgebras of \([0,1]\).
reviewed by: Daniele Mundici
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 03G25
zbMATH DE Number: 1761211
zbMATH Keywords: basic logic
zbMATH Keywords: BL-algebras
zbMATH Keywords: filters
zbMATH Keywords: variety
zbMATH Keywords: MV-algebras
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1761211