An extension of Willard?s Finite Basis Theorem: Congruence meet-semidistributive varieties of finite critical depth

Abstract

Ross Willard proved that every congruence meet-semidistributive variety of algebras that has a finite residual bound and a finite signature can be axiomatized by some finite set of equations. We offer here a simplification of Willard’s proof, avoiding its use of Ramsey’s Theorem. This simplification also extends Willard’s theorem by replacing the finite residual bound with a weaker condition.