A finite basis theorem for residually finite, congruence meet-semidistributive varieties

Abstract

We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then it is finitely based. Theorem B: there is an algorithm which, given m<w and a finite algebra in a finite language, determines whether the variety generated by the algebra is congruence meet-semidistributive and residually less then m.