From Well-Quasi-Ordered Sets to Better-Quasi-Ordered Sets

We consider conditions which force a well-quasi-ordered poset (wqo) to be betterquasi-ordered (bqo). In particular we obtain that if a poset P is wqo and the set Sω(P ) of strictly increasing sequences of elements of P is bqo under domination, then P is bqo. As a consequence, we get the same conclusion if Sω(P ) is replaced by J (P ), the collection of non-principal ideals of P , or by AM(P ), the collection of maximal antichains of P ordered by domination. It then follows that an interval order which is wqo is in fact bqo.