From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3294 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Construction of a real closure Date: Thu, 4 May 2006 11:22:10 -0400 (EDT) Message-ID: <34794.4216955968$1241019210@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 1241019210 8121 80.91.229.2 (29 Apr 2009 15:33:30 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:33:30 +0000 (UTC) To: Categories list Original-X-From: rrosebru@mta.ca Thu May 4 17:37:53 2006 -0300 X-Keywords: X-UID: 214 Original-Lines: 14 Xref: news.gmane.org gmane.science.mathematics.categories:3294 Archived-At: 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