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
Copyright
Copyright © 1999, Kluwer Academic Publishers.
Publisher
Kluwer Academic Publishers
Volume
16
Peer Reviewed
yes
Keywords
countable width, order-separable, chain, k-entangled subset, Open Col- oring Axiom
eCommons Citation
Gruenhage, Gary and Mashburn, Joe, "On The Decomposition of Order-separable Posets of Countable Width into Chains" (1999). Mathematics Faculty Publications. 25.
https://ecommons.udayton.edu/mth_fac_pub/25
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.