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Jul 29, 2016 at 13:57 vote accept Asaf Karagila
Jul 15, 2016 at 18:34 comment added Ali Enayat @AsafKaragila: I am not sure, but see the postscript that I have added to my answer.
Jul 15, 2016 at 18:33 history edited Ali Enayat CC BY-SA 3.0
Added a postscript
Jul 15, 2016 at 5:24 comment added Asaf Karagila Thanks Ali. How about when CH fails, is the answer known?
Jul 15, 2016 at 4:25 comment added Ali Enayat @FrançoisG.Dorais: GCH implies the corollary for regular $\kappa$ (by Chang's two-cardinal theorem), but for singular $\kappa$ one seems to need fine-structural facts true in the constructible universe (judging from the proof of Jensen's Gap-1 Theorem).
Jul 15, 2016 at 2:45 comment added François G. Dorais Is the corollary equivalent to GCH?
Jul 15, 2016 at 0:39 history edited Ali Enayat CC BY-SA 3.0
added 2 characters in body
Jul 14, 2016 at 23:28 history answered Ali Enayat CC BY-SA 3.0