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1. Introduction Stone, in [8], developed for distributive lattices a representation theory generalizing that for Boolean algebras. This he achieved by topologizing the set X of prime ideals of a distributive lattice A (with a zero element) by taking as a base {P a : aeA} (where P a denotes the set of prime ideals of A not containing a), and by showing that… (More)

The varietyMV of all MV-algebras is shown to be non-canonical in a strong sense. Specifically it is shown that the canonical extension of the Chang algebra, K2, is not an MV-algebra. As a consequence, no non-finitely generated variety of MV-algebras is canonical.

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)

- Brian A. Davey, Hilary A. Priestley
- Discrete Mathematics
- 1993

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)

- Hilary A. Priestley, Martin P. Ward
- J. Symb. Comput.
- 1994

A backtracking algorithm with element order selection is presented, and its efficiency discussed in relation both to standard examples and to examples concerning relation-preserving maps which the algorithm was derived to solve.

- Brian A. Davey, Miroslav Haviar, Hilary A. Priestley
- J. Symb. Log.
- 1995

L. M/trki and R. P6schel have characterised the endoprimal distributive lattices as those which are not relatively complemented. The theory of natural dualities implies that any finite algebra A on which the endomorphisms of A yield a duality on the quasivariety DSP(A) is necessarily endoprimal. This note investigates endodualisability for finite… (More)

- Mai Gehrke, Hilary A. Priestley
- Reports on Mathematical Logic
- 2008

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)