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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