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.
Anti-chain. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anti-chain&oldid=50957