Weak weak Koenig and covering spaces

[Stephen G. Simpson]

Ah, now I understand, you are asking whether any of the familiar theorems
about covering spaces need WWKL.  I don't know, good question!

On Mon, May 10, 2021 at 1:34 PM Stephen G. Simpson <sgslogic at gmail.com>
wrote:

> Well, there is my 1996 paper with Douglas Brown and Mariagnese Giusto,
> "Vitali's Theorem and WWKL."  :-)
>
> On Mon, May 10, 2021 at 1:10 PM Timothy Y. Chow <tchow at math.princeton.edu>
> wrote:
>
>> Are any basic topological theorems about covering spaces unprovable in
>> RCA_0?
>>
>> The reason I ask is that I was recently refreshing my memory about some
>> of
>> those results, and it seems that some version of the Vitali covering
>> lemma
>> is typically used when lifting a map to a covering space.  So maybe the
>> weak weak Koenig lemma is needed?
>>
>> There are some basic results about finitely generated groups that have
>> nice proofs using covering spaces.  Perhaps the simplest one is that a
>> subgroup of a free group is free.  More sophisticated examples can be
>> found in Serre's book "Trees."  Are any of these results unprovable in
>> RCA_0?
>>
>> Tim
>>
>
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