Least V-quasivarieties of MV-algebras

This paper is a contribution to the study of the lattice of all quasivarieties of MV-algebras. Given a variety V of MV-algebras, we say that a quasivariety is a V-quasivariety provided that it generates V as a variety. It turns out that every variety has a least V-quasivariety denoted by QVQV. Moreover, it is generated as a quasivariety by its free algebra over an infinite set of generators. We obtain a Komori's type characterization of QVQV for every proper subvariety of MV-algebras. We investigate the order structure of the poset of least V-quasivarieties and we find all minimal quasivarieties among all quasivarieties of MV-algebras different from the class of boolean algebras. Finally, we make some remarks on the logical interpretation of least V-quasivarieties of MV-algebras as structurally complete extensions of the infinite valued Łukasiewicz logic.