Geodesic
Distributive ordered sets and relative pseudocomplements
Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 2, pp. 163-181

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Brouwerian ordered sets generalize Brouwerian lattices. The aim of this paper is to characterize (α)-complete Brouwerian ordered sets in a manner similar to that used previously for pseudocomplemented, Stone, Boolean and distributive ordered sets. The sublattice (G(P)) in the Dedekind-Mac Neille completion (DM(P)) of an ordered set (P) generated by (P) is said to be the characteristic lattice of (P). We can define a stronger notion of Brouwerianicity by demanding that both (P) and (G(P)) be Brouwerian. It turns out that the two concepts are the same for finite ordered sets. Further, the so-called antiblocking property of distributive lattices is generalized to distributive ordered sets.
Keywords: Brouwerian ordered set, distributive ordered set, relative pseudocomplement 
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Niederle, Josef. Distributive ordered sets and relative pseudocomplements. Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 2, pp. 163-181. http://geodesic.mathdoc.fr/item/DMGAA_2006_26_2_a2/