From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3298 Path: news.gmane.org!not-for-mail From: Phil Scott Newsgroups: gmane.science.mathematics.categories Subject: Re: Construction of a real closure Date: Thu, 4 May 2006 22:14:02 -0400 (EDT) Message-ID: <6345.8725381226$1241019213@news.gmane.org> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241019212 8136 80.91.229.2 (29 Apr 2009 15:33:32 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:33:32 +0000 (UTC) To: Categories list Original-X-From: rrosebru@mta.ca Fri May 5 09:33:32 2006 -0300 X-Keywords: X-UID: 218 Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:3298 Archived-At: Dear Mike: One reference is the work of M-F Coste-Roy and H. Lombardi in Real Algebraic Geometry; a quick Google search yielded: http://hlombardi.free.fr/publis/AMega90-1.html Also they have some papers in the J.ACM, apparently. In fact, it seems to be a huge area of model theory: see http://name.math.univ-rennes1.fr/michel.coste/Borel/w1abs.html Cheers, Phil On Thu, 4 May 2006, Michael Barr wrote: > Is there a reference for the fact that a countable decidably ordered field > has a constructable (and decidably ordered) real closure? > > Maybe 20 years ago, an undergraduate did a project under my supervision > proving exactly that (although the proofs are not constructive). While I > don't think it would prove feasible for actual computation, the fact that > it exists is interesting. Finally, I have looked more closely at it and > if it is not known, I think it publishable. Unfortunately, the student > (who was a Commonwealth Fellow at Cambridge) lost interest in math and is > doing other things. But I think I know how to get in touch with him. > > Michael > > > >