
Re: Free group on m generators elementary extension of the free group on n generators (n < m)?
Posted:
Jul 9, 2013 11:40 AM


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 firstorder theory...

