[FOM] Nielsen-Schreier

[T.Forster at dpmms.cam.ac.uk]

Dear Marco.

Yes, i knew that. What i was asking was if the converse is still open: can 
one infer AC from the news that every subgroup of a free group is free? As 
far as i can tell from the traffic on FOM it is still open...


On May 21 2013, Marco Forti wrote:

>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.
>>
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