Abstract

It is an open question whether the class of BCK-algebras is generated by its finite members. As to its proper subclasses, all we know is that the answer is positive in case of any subvariety of the variety of positive implicative BCK-algebras – this result easily follows from DiegoPopiel theorem , and also in case of any subvariety of the variety of Lukasiewicz algebras – this follows from Komori’s result . The result we have proved is the following Theorem. There are at least ℵ0 varieties of commutative BCK-algebras not generated by their finite members