Canonicity in subvarieties of BL-algebras

We prove that every subvariety of BL-algebras which is not finitely generated is not σ-canonical. We also prove π-canonicity for an infinite family of subvarieties of BL-algebras that are not finitely generated. To do so we study the behavior of canonical extensions of ordered sums of posets.

Bibliographic Details
Authors: Busaniche, Manuela, Cabrer, Leonardo Manuel
Format: article
Status:Published version
Publication Date:2009
Country:Argentina
Institution:Consejo Nacional de Investigaciones Científicas y Técnicas
Repository:CONICET Digital (CONICET)
Language:English
OAI Identifier:oai:ri.conicet.gov.ar:11336/75198
Online Access:http://hdl.handle.net/11336/75198
Access Level:Open access
Keyword:Bl-Algebras
Canonicity
Residuated Lattices
Completions of Algebras
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Description
Summary:We prove that every subvariety of BL-algebras which is not finitely generated is not σ-canonical. We also prove π-canonicity for an infinite family of subvarieties of BL-algebras that are not finitely generated. To do so we study the behavior of canonical extensions of ordered sums of posets.