Timeline for Can $Ord$ have nontrivial second-order elementary self-embeddings?

8 events

when toggle format	what		by	license	comment
Dec 15, 2020 at 20:56	comment	added	Noah Schweber		This is a great answer, thanks!
Dec 15, 2020 at 20:56	vote	accept	Noah Schweber
Dec 15, 2020 at 20:44	history	edited	Gabe Goldberg	CC BY-SA 4.0	added 556 characters in body
Dec 15, 2020 at 6:21	history	edited	Gabe Goldberg	CC BY-SA 4.0	added 407 characters in body
Dec 15, 2020 at 2:07	comment	added	Gabe Goldberg		@AsafKaragila If you want to get a model of NBG with one of these embeddings, a $j : V_{\lambda+2}\to V_{\lambda+2}$ is not going to work. Or an inaccessible $\kappa$ with a second order embedding $\kappa\to \kappa$. Feels like you're gonna need something like Reinhardt with proper class of Lowenheim-Skolems. (Of course it's even more reasonable to doubt the consistency of super-Reinhardt cardinals.)
Dec 15, 2020 at 1:56	comment	added	Asaf Karagila♦		I mean, a super-Reinhardt implies there is a Reinhardt with a proper class of LS cardinals. No? In some sense an I3 is already "kinda" that. And if you want a 2nd order embedding, then Kunen cardinals (critical points of $j\colon V_{\lambda+2}\prec V_{\lambda+2}$, where $\kappa=\operatorname{crit}(j)$ and $\lambda=\sup j^n(\kappa)$) already kind of supply this situation to you, and the consistency of a Kunen cardinal is already bounded by I0.
Dec 15, 2020 at 0:45	history	edited	Gabe Goldberg	CC BY-SA 4.0	added 140 characters in body
Dec 15, 2020 at 0:40	history	answered	Gabe Goldberg	CC BY-SA 4.0