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.
@article{1183746015,
author = {Willard, Ross},
title = {A Finite Basis Theorem for Residually Finite, Congruence Meet-Semidistributive Varieties},
journal = {J. Symbolic Logic},
volume = {65},
number = {1},
year = {2000},
pages = { 187-200},
language = {en},
url = {http://dml.mathdoc.fr/item/1183746015}
}
Willard, Ross. A Finite Basis Theorem for Residually Finite, Congruence Meet-Semidistributive Varieties. J. Symbolic Logic, Tome 65 (2000) no. 1, pp. 187-200. http://gdmltest.u-ga.fr/item/1183746015/