Study of canonicity in subvarieties of BL-algebras

Abstract

We prove that every subvariety of BL-algebras which is not finitely generated is not $\sigma$-canonical. We also prove $\pi$-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.

Accepted: Algebra Universalis.