Tabular and Pretabular Varieties of MTL-Algebras

Tabular logics have been studied since the sixties, while the notion of pretabular (PT) variety was firstly introduced in the seventies by A.V. Kuznetsov and L. Maksimova, for Heyting algebras. A variety is tabular whenever it is generated by one finite algebra. A variety \(\mathbb {L}\) is PT whenever \(\mathbb {L}\) is not tabular but every variety \(\mathbb {M}\subsetneq \mathbb {L}\) is tabular. In this paper we study the same notion for the case of MTL-algebras. We show that a variety of MTL-algebras is PT if and only if it is generated by each of its infinite chains, and we study some general properties of PT varieties of MTL-algebras. Also, we provide a full classification of tabular and PT varieties of BL and WNM-algebras.