Finitely generated upper set
= Finitely generated upper set
{title2=$\uparrow A,\quad |A|<\infty$}
An <upper set> generated by a finite <set> $A$ is represented by the <minimal elements> of $A$. Removing a nonminimal generator preserves the upward closure. If each pair has a <least upper bound>, then $\uparrow A\cap\uparrow B=\uparrow\{a\vee b:a\in A,b\in B\}$, so finite generators support <intersection> without enumerating the potentially infinite represented <sets>.