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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 14, 2013 5:45 AM
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Butch Malahide wrote:
> On Tuesday, July 9, 2013 5:39:00 AM UTC-5, Sandy 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?
>
> I guess you meant to say that n > 1.


Indeed I did! (And I thought I'd acknowledged that elsewhere, but the
post, and the post I was replying to, have disappeared. Perhaps I
dreamt it.) Btw, I have since found that this is problem 3 at the back
of Chang & Keisler's /Model Theory/. I have the second edition, maybe
subsequent editions solve it or at least give reference to its solution



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