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

摘要

We consider conditions which force a well-quasi-ordered poset (wqo) to bebetter-quasi-ordered (bqo). In particular we obtain that if a poset $P$ is wqoand the set $S_{\omega}(P)$ of strictly increasing sequences of elements of $P$is bqo under domination, then $P$ is bqo. As a consequence, we get the sameconclusion if $S_{\omega} (P)$ is replaced by $\mathcal J^1(P)$, the collectionof non-principal ideals of $P$, or by $AM(P)$, the collection of maximalantichains of $P$ ordered by domination. It then follows that an interval orderwhich is wqo is in fact bqo.