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From well-quasi-ordered sets to better-quasi-ordered sets | | Maurice Pouzet
; Norbert Sauer
; | | Date: |
6 Jan 2006 | | Subject: | Combinatorics; Logic | | 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 $S_{omega}(P)$ 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. | | Source: | arXiv, math/0601119 | | Services: | Forum | Review | PDF | Favorites | |
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