Canonicity in subvarieties of BL-algebras
Canonical extensions were introduced by Jonsson and Tarski for Boolean algebras with operators and generalized for distributive lattices, lattices and posets with different internal operations. They provide an algebraic formulation of what is otherwise treated via topological duality or relational methods. In this paper, the authors study \(\sigma\)- and \(\pi\)-canonicity for subvarieties of BL-algebras. They prove that every subvariety of BL-algebras that is not finitely generated is not \(\sigma\)-canonical. Also, they prove \(\pi\)-canonicity for an infinite family of subvarieties of BL-algebras that are not finitely generated.
scientific article; zbMATH DE number 5782714