Abstract

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