From well-quasi-ordered sets to better-quasi-ordered sets

Abstract

We consider conditions which force a well-quasi-ordered poset (wqo) to be better-quasi-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.