Realizer

A Set $R$ of Linear Extensions of a Poset $P = (X, \leq)$ is a realizer of $P$ (and is said to realize $P$) provided that for all $x,y \in X$, $x \leq y$ Iff $x$ is below $y$ in every member of $R$.

See also Dominance, Linear Extension, Partially Ordered Set, Poset Dimension