[FOM] Nielsen-Schreier

[Marco Forti]

Dear Thomas,
P.Howard proved the following, in a paper on JSL 1985:
(i) NS implies ACfin
(ii)NSN implies AC

[NSN states that there exists a set of free generators with a property
 obtained in the known algebraic proofs of NS, so AC implies NSN]
The equivalence of NSN and NS is listed as unknown in the book
of Howard and Rubin of 1991.

Best wishes, Marco

On Tue, May 7, 2013 at 2:13 PM, <T.Forster at dpmms.cam.ac.uk> wrote:

> Doing some homework in preparation for a second edition of *Logic,
> Induction and Sets* and find myself wondering whether or not it is still
> open whether or not NS implies choice. The internet gives no clue.
>
>       tf
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-- 
Marco Forti
Dipartimento di Matematica
Universita' di Pisa
V. Buonarroti 1 C - 56100 PISA (Italy)
Tel. +39 050 2213876 (direct)
       +39 050 2213801 (operator)
Fax  +39 050 2213813
e-mail forti at dma.unipi.it
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