Anti-chain

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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 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.