Distributive Ordered Sets and Relative Pseudocomplements
نویسنده
چکیده
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.
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