OPTIMAL NATURAL DUALITIES

The authors showed previously that for each of the varieties B" (3 < n < w) of pseudocomplemented distributive lattices there exists a natural du- ality given by a set of p(n) + 3 binary algebraic relations, where p(n) denotes the number of partitions of n . This paper improves this result by establishing that an optimal set of n + 3 of these relations suffices. This is achieved by the use of "test algebras": it is shown that redundancy among the relations of a duality for a prevariety generated by a finite algebra may be decided by testing the duality on the relations, qua algebras.