Busaniche, M and Cabrer, L., "Study of canonicity in subvarieties of BL-algebras", to appear in Algebra Universalis.

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.