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Topic: Free group on m generators elementary extension of the free group on n generators (n < m)?
Replies: 11   Last Post: Jul 15, 2013 1:13 PM

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Sandy

Posts: 51
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
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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 first-order 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).



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