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AAA60: Workshop on General Algebra (60. Arbeitstagung Allgemeine Algebra)
June 22-25, 2000
Dresden University of Technology
Dresden, Germany

Organizers
Reinhard Pöschel, Manfred Droste, Bernhard Ganter

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On pseudocomplemented and Stone ordered sets
by
Josef Niederle
Masarykova universita, Brno

The aim of this paper is to characterize both the pseudocomplemented and Stone ordered sets in a manner similar to that used in a previous paper for Boolean and distributive ordered sets. The sublattice G(A) of the Dedekind-Mac Neille completion DM(A) of an ordered set A generated by A is said to be the characteristic lattice of A. We will show that there are distributive pseudocomplemented ordered sets whose characteristic lattices are not pseudocomplemented. We can define a stronger notion of pseudocomplementedness by demanding that both A and G(A) be pseudocomplemented. It turns out that the two concepts are the same for finite and Stone ordered sets.

Date received: May 16, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-32.