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Timeline for Measurability and Axiom of choice

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Jul 14, 2015 at 13:00 comment added Joel David Hamkins For example, it is consistent with ZF that $\mathbb{R}$ is a countable union of countable sets, and in this case every set of reals is Borel. So one needs at least some AC to prove even that there are any non-Borel sets at all, let alone non-Borel analytic sets.
Jul 14, 2015 at 12:19 comment added Matthias Ludewig Sorry, I meant to write Lebesgue-measurable.
Jul 14, 2015 at 12:12 history answered Gerald Edgar CC BY-SA 3.0