Date: Jul 9, 2013 11:40 AM
Author: David C. Ullrich
Subject: Re: Free group on m generators elementary extension of the free group on n generators (n < m)?
On Tue, 09 Jul 2013 11:39:00 +0100, Sandy <sandy@hotmail.invalid>

wrote:

>For n, m natural numbers, n < m, let G be the free group on n generators

>and H the free group on m generators. Is H an elementary extension of G?

Assuming that the generators for G are a subset of the generators

for H, so that H _is_ an extension of G:

I've seen it said

http://en.wikipedia.org/wiki/Free_group#Universal_property

that any two free groups have the same first-order theory...