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''Sperner family''

A set $A$ of elements of a [[partially ordered set]] $(S,\le)$ which are incomparable: for $x \neq y$ in $A$, neither $x \le y$ nor $y \le x$ holds.  The [[width of a partially ordered set]] is the the largest size of an antichain.

A ''Sperner family'' is a collection of sets which form an anti-chain with respect to set inclusion.  See also [[Sperner property]].