Timeline for Can an ultrapower be undone by class forcing?
Current License: CC BY-SA 3.0
8 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Jan 15, 2017 at 16:27 | vote | accept | Noah Schweber | ||
| Jan 15, 2017 at 15:57 | answer | added | Joel David Hamkins | timeline score: 5 | |
| Jan 15, 2017 at 12:14 | comment | added | Joel David Hamkins | I was merely responding to your statement, "...resurrecting the measurability of a smaller cardinal. If that's even possible...". It is possible, by Kunen's theorem. I agree that this does not shed light on Noah's question. | |
| Jan 15, 2017 at 12:10 | comment | added | Asaf Karagila♦ | @Joel: Yes, by adding Cohen sets below the measurable, I know (and this way it ends up immune to Cohen sets). But never the less, this is a very different situation from taking an inner model which is an ultrapower by a measure. | |
| Jan 15, 2017 at 12:00 | comment | added | Joel David Hamkins | @AsafKaragila Kunen showed long ago that a non-measurable cardinal can become measurable in a forcing extension, and the consistency strength is just a measurable cardinal. You start with $\kappa$ measurable, and then kill it in a way that it can be resurrected. | |
| Jan 15, 2017 at 6:51 | comment | added | Asaf Karagila♦ | Well, undoing an ultrapower means resurrecting the measurability of a smaller cardinal. If that's even possible, I'd imagine some very very large cardinals are involved; and the measure being something like some type of a huge measure or so. | |
| Jan 15, 2017 at 3:22 | history | asked | Noah Schweber | CC BY-SA 3.0 |