linguistic:paraphrasing, structural:scholar_edition
Sperner families

An antichain in the inclusion ordering of subsets of an n {\displaystyle n} -element set is known as a Sperner family. The number of different Sperner families is counted by the Dedekind numbers, the first few of which numbers are

Even the empty set has two antichains in its power set: one containing a single set (the empty set itself) and one containing no sets.