Timeline for When does Vopěnka's principle hold?

8 events

when toggle format	what		by	license	comment
Apr 23, 2015 at 11:15	comment	added	Joel David Hamkins		@MihaHabič Great idea! But we should take an elementary substructure in a much larger $L_\theta$, since the $s_n$ are not necessarily in $L_{\delta^+}$. The point should be that by condensation, it collapses down into $L_{\delta^+}$, and gives a counterexample to well-foundedness there, which is a contradiction.
Apr 23, 2015 at 3:12	comment	added	Miha Habič		Very nice. In the $(1\to 2)$ direction of the proof you could avoid the appeal to Jensen covering by collapsing an elementary substructure of $L_{\delta^+}$ containing $\kappa$ and the $s_n$ to get an ill-foundedness already in the ultrapower of $L_{\delta^+}$.
Apr 23, 2015 at 3:09	history	edited	Joel David Hamkins	CC BY-SA 3.0	edited body
Apr 23, 2015 at 3:00	comment	added	Joel David Hamkins		@MarianoSuárez-Alvarez I added a link in the post to zero sharp on Wikipedia. It is a large cardinal axiom that is equivalent to the existence of a nontrivial elementary embedding $j:L\to L$, but also has a characterization in terms of the existence of robust order-indiscernibles for the constructible universe.
Apr 23, 2015 at 2:59	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 1289 characters in body
Apr 23, 2015 at 2:55	comment	added	Mariano Suárez-Álvarez		What is $0^\sharp$? :-\|
Apr 22, 2015 at 18:42	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 57 characters in body
Apr 22, 2015 at 18:37	history	answered	Joel David Hamkins	CC BY-SA 3.0