The paper considers a generalization of the standard completion of a partially ordered set through the collection of all its lower sets.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1119, author = {Sergey A. Solovyov}, title = {Completion of partially ordered sets}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {26}, year = {2006}, pages = {59-67}, zbl = {1141.18005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1119} }
Sergey A. Solovyov. Completion of partially ordered sets. Discussiones Mathematicae - General Algebra and Applications, Tome 26 (2006) pp. 59-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1119/
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