
Re: Orderpreserving embeddings of ordinals in the real numbers
Posted:
Jul 28, 2006 2:00 PM


In article <eadai0$g34$1@news.ks.uiuc.edu>, David Madore <david.madore@ens.fr> wrote:
> > Which ordinals can we do this for? > > If you're asking which ordinals are orderisomorphic to a subset of > the real numbers, the answer is simple (at least, assuming the axiom > of choice): exactly the countable ordinals.
And more generally: any countable totally ordered set can be imbedded in the rationals.
 G. A. Edgar http://www.math.ohiostate.edu/~edgar/

