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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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David C. Ullrich

Posts: 3,109
Registered: 12/13/04
Re: Free group on m generators elementary extension of the free group on n generators (n < m)?
Posted: Jul 9, 2013 11:40 AM
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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...






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