Hoare domination preorder
= Hoare domination preorder
{c}
{title2=$S\le_H T$}
For subsets of a <preorder>, Hoare domination means every source element has some greater or equal target element: $S\le_H T\iff\forall s\in S\;\exists t\in T\;(s\le t)$. It is reflexive and transitive. If the base is a <well-quasi-ordering>, its finite subsets are <well-quasi-ordered> by this relation; arbitrary subsets need not be, as the <Rado order> shows.