Subvarieties of BL-algebras generated by single-component chains
type: Item
instance of: scholarly article
title: Subvarieties of BL-algebras generated by single-component chains
zbMATH Open document ID: 1023.03060
author: Antonio Di Nola
author: Francesc Esteva
author: Pere García
author: Lluís Godo
author: Salvatore Sessa
published in: Archive for Mathematical Logic
publication date: 2003-09-16T00:00:00Z
review text: In this paper we study and equationally characterize the subvarieties of \textbf{BL}, the variety of BL-algebras, which are generated by families of single-component BL-chains, i.e. MV-chains, product-chains or Gödel-chains. Moreover, it is proved that they form a segment of the lattice of subvarieties of \textbf{BL} which is bounded by the Boolean variety and the variety generated by all single-component chains, called \textbf{Ł}\(\mathbf{\Pi}\)\textbf{G}. Finally, we prove that all their corresponding logics are semi-standard complete.
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03B50
zbMATH DE Number: 1982494
zbMATH Keywords: semi-standard complete logics
zbMATH Keywords: subvarieties
zbMATH Keywords: variety of BL-algebras
zbMATH Keywords: single-component chains
reviewed by: Salvatore Sessa
MaRDI profile type: Publication
full work available at URL: s001530100114
OpenAlex ID: W2030856324
DOI: 10.1007/S001530100114
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description: scientific article; zbMATH DE number 1982494