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

2006/01/06 by Pouzet, Maurice, Sauer, Norbert
#03E04 #06A06 #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.math/0601119

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_ω(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_ω (P) is replaced by \mathcal J¹(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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