A Finite Basis Theorem for Residually Finite, Congruence Meet-Semidistributive Varieties

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 < 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.

• Type: Journal
• Year: 2000
• Where: JSYML
• Authors: Ross Willard
• Keywords: Congruence Meet-semidistributivity, Finite Cardinal, Finite Language, JSYML 2000