A Representation Theorem for Semilattices
Dmitry Aleksandrovich Bredikhin · Proceedings of the American Mathematical Society · 1984
We prove that every semilattice $(L, \wedge )$ admits an embedding $Q$ into the set $R(X)$ of all partial orders on some set $X$ such that for all $a$, $b \in L$, $Q(a \wedge b) = Q(a) \cap Q(b)$ and if $a \vee b$ exists then also $Q(a \vee b) = Q(b) \circ Q(a)$.