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.
Copyright © 1999, Kluwer Academic Publishers.
Kluwer Academic Publishers
countable width, order-separable, chain, k-entangled subset, Open Col- oring Axiom
Gruenhage, Gary and Mashburn, Joe, "On The Decomposition of Order-separable Posets of Countable Width into Chains" (1999). Mathematics Faculty Publications. 25.