We define a natural ordering on the power set 𝔓(Q) of any finite partial order Q, and we characterize those partial orders Q for which 𝔓(Q) is a distributive lattice under that ordering.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1046,
author = {Martin R. Goldstern and Dietmar Schweigert},
title = {Power-ordered sets},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {22},
year = {2002},
pages = {39-46},
zbl = {1037.06002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1046}
}
Martin R. Goldstern; Dietmar Schweigert. Power-ordered sets. Discussiones Mathematicae - General Algebra and Applications, Tome 22 (2002) pp. 39-46. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1046/
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[001] [2] J. Naggers and H.S. Kim, Basic Posets, World Scientific Publ. Co., River Edge, NJ, 1998.