Hilary A. Priestley

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A construction of canonical extensions of Stone algebras is presented that uses the natural duality based on the three-element generating algebra 3 rather than the Priestley duality based on 2 that is traditionally used to build the canonical extension. The new approach has the advantage that the canonical extension so constructed inherits its algebra(More)
A natural dl:sitty is obtained for each finitely generated variety B,, (n < CG) of distributive p-algebras. 7 he duality for B,, is based on a schizophrenic object: E:, in B,, is the algebra 2” @ 1 which gencrates the b:uiety and c?, is a topological relationai structure carrying the discrete topology and a set of Qcbraic reititions. The relations arc (i)(More)
A b s t r a c t. The purpose of this note is to expose a new way of viewing the canonical extension of posets and bounded lattices. Specifically, we seek to expose categorical features of this completion and to reveal its relationship to other completion processes. The theory of canonical extensions is introduced by Jónsson and Tarski [15, 16] for Boolean(More)