Timeline for GCH implies acceptability

7 events

when toggle format	what		by	license	comment
Jun 21, 2020 at 22:02	comment	added	Rodrigo Freire		Nice comment, thanks.
Jun 21, 2020 at 18:54	comment	added	Gabe Goldberg		Given GCH, for any infinite cardinal $\kappa$, $H_\kappa = J_\kappa^A$ for some $A\subseteq \kappa$ such that for any limit ordinals $\tau\leq \alpha < \kappa$, if $P(\tau)\cap J_{\alpha+\omega}^A\nsubseteq J_{\alpha}^A$, then there is a surjection from $\tau $ to $J_{\alpha}^A$ in $J_{\alpha+\omega}^A$. With Global Choice, one gets a class $A$ with this property such that $V = L[A]$. It seems harder to design $A = (A_\alpha)_{\alpha\in \text{Lim}}$ so that $A_\alpha$ is amenable to $J_\alpha^A$. Schindler's Set Theory, Ex 11.1 suggests this is possible, so maybe Ralf knows the answer.
Jun 20, 2020 at 14:49	history	edited	Rodrigo Freire	CC BY-SA 4.0	added 221 characters in body
Jun 20, 2020 at 8:19	history	edited	Martin Sleziak		added the (gch) tag
Jun 20, 2020 at 7:00	answer	added	Mohammad Golshani		timeline score: 4
Jun 19, 2020 at 16:25	history	edited	LSpice	CC BY-SA 4.0	Links to references; proofreading
Jun 19, 2020 at 16:13	history	asked	Rodrigo Freire	CC BY-SA 4.0