Re: Construction of a real closure

[Phil Scott <phil@site.uottawa.ca>]

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
>
>
>
>