  We prove that every clone of operations on a finite set A, if it contains a
Malcev operation, is finitely related -- i.e., identical with the clone of all
operations respecting R for some finitary relation R over A. It follows that
for a fixed finite set A, the set of all such Malcev clones is countable. This
completes the solution of a problem that was first formulated in 1980, or
earlier: how many Malcev clones can finite sets support? More generally, we
prove that every finite algebra with few subpowers has a finitely related clone
of term operations. Hence modulo term equivalence and a renaming of the
elements, there are only countably many finite algebras with few subpowers, and
thus only countably many finite algebras with a Malcev term.
