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Nov 26, 2017 at 16:35 comment added Dmytro Taranovsky @YairHayut $ω_1$-Erdős cardinal does not imply closure under sharps above it, but I think it implies closure under sharps below it, and in any case has a higher consistency strength.
Nov 26, 2017 at 11:01 comment added Yair Hayut I thought that $\omega_1$-Erdos only implies that $\forall x\in \mathbb{R}$, $x^{\#}$ exists, and not the full closure under sharps.
Nov 26, 2017 at 8:51 vote accept Julian Barathieu
Nov 26, 2017 at 2:57 history answered Dmytro Taranovsky CC BY-SA 3.0