ZFC vs ZF

[Buzzard, Kevin M]

What about an arbitrary statement in modern mathematics like the Poincare conjecture or the local Langlands conjectures? Anything which uses analysis (which these statements do) will almost certainly use at least countable dependent choice (at least in the presentation of the results in the literature, because the mathematicians working in these areas will not in general be interested in whether their uses of AC are essential).

Kevin
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From: FOM <fom-bounces at cs.nyu.edu> on behalf of JOSEPH SHIPMAN <joeshipman at aol.com>
Sent: 27 September 2021 05:16
To: Foundations of Mathematics <fom at cs.nyu.edu>
Subject: ZFC vs ZF


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Is there any well-known theorem of ZFC for which it is an open question whether it is a theorem of ZF?

Nothing involving large cardinals, please, I already know it is open whether you need choice to refute certain statements about embedding ranks into themselves.

— JS

Sent from my iPhone
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