Weak weak Koenig and covering spaces

[Stephen G. Simpson]

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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