From well-quasi-ordered sets to better-quasi-ordered sets
The electronic journal of combinatorics, Tome 13 (2006)
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 ${\cal J}^{\neg \downarrow\hskip -2pt }(P)$, 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.
@article{10_37236_1127,
author = {Maurice Pouzet and Norbert Sauer},
title = {From well-quasi-ordered sets to better-quasi-ordered sets},
journal = {The electronic journal of combinatorics},
year = {2006},
volume = {13},
doi = {10.37236/1127},
zbl = {1110.06002},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1127/}
}
Maurice Pouzet; Norbert Sauer. From well-quasi-ordered sets to better-quasi-ordered sets. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1127
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