Ordered sets with no chains of ideals of a given type

@article{Pouzet1984OrderedSW,
  title={Ordered sets with no chains of ideals of a given type},
  author={Maurice Pouzet and Nejib Zaguia},
  journal={Order},
  year={1984},
  volume={1},
  pages={159-172}
}
We study the possible order types of chains of ideals in an ordered set. Our main result is this. Given an indecomposable countable order type α, there is a finite listA1α, ...,Anα of ordered sets such that for every ordered setP the setJ(P) of ideals ofP, ordered by inclusion, contains a chain of type α if and only ifP contains a subset isomorphic to one of theA1#x03B1;, ...,Anα. The finiteness of the list relies on the notion of better quasi-ordering introduced by Nash-Williams and the… CONTINUE READING

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