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Nov 9, 2021 at 18:01 comment added Alessandro Codenotti @Accumulation Since it is consistent with $\mathsf{ZF}$ that all subsets of $\Bbb R$ are Borel and the existence of such a Borel set is open, it must be open whether $\mathsf{ZF}$ proves that such a set exists as well
Nov 8, 2021 at 20:56 comment added Wojowu @Acccumulation Yes, more specifically on a well-ordering of $\mathbb R$. I'm not aware of a choiceless construction.
Nov 8, 2021 at 20:51 comment added Acccumulation Does this construction depend on Choice?
Nov 8, 2021 at 3:22 comment added LMP Thanks for your answers.
Nov 7, 2021 at 17:07 history edited Wojowu CC BY-SA 4.0
added 13 characters in body
Nov 7, 2021 at 15:52 vote accept LMP
Nov 7, 2021 at 14:37 history answered Wojowu CC BY-SA 4.0