Geodesic
Power-ordered sets
Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 1, pp. 39-46.

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We define a natural ordering on the power set (Q) of any finite partial order Q, and we characterize those partial orders Q for which (Q) is a distributive lattice under that ordering.
Keywords: partial order, chain, linear order, antichain, power set, power-ordered set, distributive lattice, anti-automorphism 
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Goldstern, Martin; Schweigert, Dietmar. Power-ordered sets. Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 1, pp. 39-46. http://geodesic.mathdoc.fr/item/DMGAA_2002_22_1_a3/

[1] J.C. Abbott, Sets, Lattices and Boolean Algebras, Allyn Bacon, Inc., Boston, MA, 1969.

[2] J. Naggers and H.S. Kim, Basic Posets, World Scientific Publ. Co., River Edge, NJ, 1998.