Optimal Natural Dualities
Brian Davey, H. A. Priestley · Transactions of the American Mathematical Society · 1993
The authors showed previously that for each of the varieties ${{\mathbf {B}}_n}(3 \leq n < \omega )$ of pseudocomplemented distributive lattices there exists a natural duality 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.