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Apr 22, 2021 at 8:35 comment added Joel David Hamkins @BenjaminSteinberg The $\Sigma_1$-correctness was only for the very general fact. Meanwhile, the example at the end of my other answer produces a ZFC independent instance assuming only Con(ZFC), which is required in order to have anything independent of ZFC.
Apr 22, 2021 at 6:43 vote accept CommunityBot
Apr 22, 2021 at 2:11 comment added Benjamin Steinberg But the independence from ZFC thing seems to make some assumptions about cardinals
Apr 21, 2021 at 20:22 history answered Joel David Hamkins CC BY-SA 4.0