Timeline for Equivalent definitions of Woodin cardinals in $\operatorname{ZFC}_{-}/\operatorname{ZFC}^{-}$

6 events

when toggle format	what		by	license	comment
Dec 25, 2016 at 23:24	history	edited	Stefan Mesken	CC BY-SA 3.0	added 518 characters in body
Dec 25, 2016 at 23:19	history	edited	Stefan Mesken	CC BY-SA 3.0	added 518 characters in body
Dec 25, 2016 at 21:39	comment	added	Joel David Hamkins		I'm sorry, but I don't really understand your reply. How does it make sense to assume MK if the question is about the effects of assuming only ZFC-, a much weaker theory? My question was about the meaning of statement 1 in ZFC-, since it doesn't seem formalizable as you have stated it.
Dec 25, 2016 at 20:50	comment	added	Joel David Hamkins		Can you clarify what you mean in 1 by saying "there is a definable j..."? The concept of "definable" is not expressible in first-order set theory, but I think you intend for this definition to be formalized in ZFC. I guess you mean that $j$ is a class, and you can make it first-order by going to the induced extender. But in a ZFC- context, it isn't clear what you would mean. Do you still insist the embedding is definable even when, say, the power set axiom fails badly?
Dec 25, 2016 at 20:44	history	edited	Stefan Mesken	CC BY-SA 3.0	deleted 20 characters in body
Dec 25, 2016 at 20:15	history	asked	Stefan Mesken	CC BY-SA 3.0