Timeline for Coherent sequence of ultrafilters in iterated forcing extensions
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 10 at 23:19 | comment | added | Joel David Hamkins | You will get a positive answer if $\delta$ has cofinality bigger than $\kappa$ and the subsets of $\kappa$ are all added individually by some stage, since then the union of the $U_\alpha$ for $\alpha<\delta$ simply will be a $\kappa$-complete ultrafilter in the extension. | |
| Jul 10 at 22:12 | comment | added | Monroe Eskew | I had a thought on this. What if at each stage you add a stationary set that is almost contained in every set from some measure on κ? If κ remains strongly compact, then the nonstationary ideal restricted to this set can be extended to a measure in the extension. Then repeat. At limit stages try to show that the special stationary sets you add at each stage have stationary intersection. Starting from an indestructible supercompact, I think this can be done with iterated Levy collapses and the limit stage claim should hold at small cofinalities. I’m not sure if this helps with your goal. | |
| Jul 10 at 21:55 | answer | added | Joel David Hamkins | timeline score: 3 | |
| Jul 10 at 21:31 | history | edited | Tristan vd Vlugt | CC BY-SA 4.0 |
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| Jul 10 at 21:22 | history | asked | Tristan vd Vlugt | CC BY-SA 4.0 |