Critically prime interval orders (Q998455)

If \(P=(V,\leq )\) is an ordered set and \(A\subseteq V\), then \(A\) is called autonomous in \(P\) if for all \(v\not\in A\) and for all \(a,a'\in A\): \((v<a\Rightarrow v<a')\) and \((a<v\Rightarrow a'<v)\). An ordered set is called prime if all its autonomous subsets are trivial. The author deals with prime interval orders and with the existence of their prime upper covers.