Maltsev conditions and relations on algebras

Abstract

We show that every sentence preserved by products in a purely relational first order language corresponds to a Maltsev condition on subalgebras of direct powers. Moreover, we establish that this correspondence captures all strong Maltsev conditions whose defining equations do not involve compositions. We then demonstrate how a broader version of the correspondence is sufficient to capture all Maltsev conditions when we restrict our attention to locally finite varieties.