A Characterization of Idempotent Strong Mal’cev Conditions for Congruence Meet-Semidistributivity in Locally Finite Varieties

We prove a characterization of all idempotent, linear, strong Mal’cev conditions in two variables which hold in all locally finite congruence meet-semidistributive varieties. This is an alternative proof to the one previously given by Z. Brady, and has some advantages, some disadvantages, to his approach. Along the way we prove that such a strong Mal’cev condition holds in all locally finite congruence meet-semidistributive varieties iff it is realized in a certain four-element algebra.