Sandy
Posts:
48
Registered:
7/9/13


Re: Free group on m generators elementary extension of the free group on n generators (n < m)?
Posted:
Jul 9, 2013 11:56 AM


dullrich@sprynet.com wrote: > 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...
Thank you. That's a useful link, because here: http://en.wikipedia.org/wiki/Free_group#Tarski.27s_problems, are references to the solution that Rupert McCallum mentioned (the Google page for Rupert's URL tells me I've exceeded my limit of something or other).

