Finite model property and varieties of BL-algebras (Q2233195)

The notion of BL-algebras was introduced by \textit{P. Hájek} [Metamathematics of fuzzy logic. Dordrecht: Kluwer Academic Publishers (1998; Zbl 0937.03030)] as the algebraic semantics of the basic logic BL, the logic of all continuous t-norms and their residua. A variety of BL-algebras has the finite model property, if it is generated by its finite chains. The paper mainly studies the finite model property for varieties of BL-algebras. The complete classification of the finite model property for those varieties of BL-algebras which are generated by a finite class of chains with finitely-many components is given. For the entire collection see [Zbl 1470.68020].