A finite basis theorem for difference-term varieties with a finite residual bound

Abstract

We prove that if V \mathcal V is a variety of algebras (i.e., an equationally axiomatizable class of algebraic structures) in a finite language, V \mathcal V has a difference term, and V \mathcal V has a finite residual bound, then V \mathcal V is finitely axiomatizable. This provides a common generalization of R. McKenzie’s finite basis theorem for congruence modular varieties with a finite residual bound, and R. Willard’s finite basis theorem for congruence meet-semidistributive varieties with a finite residual bound.