Optimal natural dualities

Davey, B. A.; Priestley, H. A.

doi:10.1090/S0002-9947-1993-1169079-7

Optimal natural dualities
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by B. A. Davey and H. A. Priestley PDF

Trans. Amer. Math. Soc. 338 (1993), 655-677 Request permission

Abstract:

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.

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