From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3295 Path: news.gmane.org!not-for-mail From: "Marta Bunge" Newsgroups: gmane.science.mathematics.categories Subject: RE: Construction of a real closure Date: Thu, 04 May 2006 18:20:08 -0400 Message-ID: <37303.3429765657$1241019211@news.gmane.org> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; format=flowed X-Trace: ger.gmane.org 1241019210 8124 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: mbarr@math.mcgill.ca, categories@mta.ca Original-X-From: rrosebru@mta.ca Fri May 5 09:31:07 2006 -0300 X-Keywords: X-UID: 215 Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:3295 Archived-At: Dear Michael, >Is there a reference for the fact that a countable decidably ordered field >has a constructable (and decidably ordered) real closure? > In my paper "Sheaves and Prime Model Extensions", J. of Algebra 68 (1981) 79-96, there is a proof of the existence of the real closure of an ordered field in any elementary topos, plus considerations about the failure of the existence of the algebraic closure. The context is more general (model theory in toposes), and there are other instances which I do not recall offhand. Maybe that is not what you are asking? I thought that I would mention it, just in case. Best, Marta