Document Type

Article

Publication Date

1999

Publication Source

Order

Abstract

partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring Axiom.

Inclusive pages

171-177

ISBN/ISSN

0167-8094

Document Version

Postprint

Comments

Article available for download is the authors' accepted manuscript, made available in compliance with publisher policies on self-archiving. Some differences may exist between this version and the published version; as such, researchers wishing to quote directly from this source are advised to consult the version of record, available online from the publisher.

Permission documentation is on file.

Publisher

Kluwer Academic Publishers

Volume

16

Peer Reviewed

yes

Keywords

countable width, order-separable, chain, k-entangled subset, Open Col- oring Axiom

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