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

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

2006-01-06

arxiv.org/abs/math/0601119v1

Mathematics

Combinatorics

31 pages

Scientific paper

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 $S_{\omega}(P)$ of strictly increasing sequences of elements of $P$ is bqo under domination, then $P$ is bqo. As a consequence, we get the same conclusion if $S_{\omega} (P)$ is replaced by $\mathcal J^1(P)$, 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.

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