We derive a Mal'cev condition for congruence meet-semidistributivity and th
en use it to prove two theorems. Theorem A: if a variety in a finite langua
ge is congruence meet-semidistributive and residually less than some finite
cardinal, then it is finitely based. Theorem a: there is an algorithm whic
h. given m < omega and a finite algebra in a finite language, determines wh
ether the variety generated by the algebra is congruence meet-semidistribut
ive and residually less than m.