H. Andr\'eka, I. Hodkinson, I. N\'emeti

Finite algebras of relations are representable on finite sets

Using a combinatorial theorem of Herwig on extending partial isomorphisms
of relational structures, we give a simple proof that certain classes of
algebras, including {\sf Crs}, polyadic {\sf Crs}, and {\sf WA}, have the
`finite base property' and have decidable universal theories, and that any
finite algebra in each class is representable on a finite set.