Timeline for Collapse successor of singular while preseving supercompactness
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 3, 2020 at 16:03 | comment | added | Monroe Eskew | @AsafKaragila Paul Larson’s book. | |
| Sep 3, 2020 at 15:36 | comment | added | Asaf Karagila♦ | @Monroe: Do you have a good reference for that? | |
| Sep 3, 2020 at 9:57 | comment | added | Monroe Eskew | The point is that $\kappa$ is supercompact in the generic ultrapower by elementarity, but with the proper-class tower, the ultrapower is the generic extension. | |
| Sep 3, 2020 at 9:53 | comment | added | Monroe Eskew | @JiachenYuan Yes that should be true. But it’s possible that you need to add the full proper-class sized generic to restore supercompactness. | |
| Sep 3, 2020 at 8:45 | comment | added | Jiachen Yuan | @MonroeEskew, will it make a big difference? If there are proper class of Woodin cardinal isn't it true by density argument that the class forcing factorize at some initial segment $P_{\lambda}$ for some Woodin cardinal $\lambda$? | |
| Sep 3, 2020 at 6:48 | comment | added | Monroe Eskew | You can use the proper class version of the stationary tower. Do you want a set-sized forcing? | |
| Sep 3, 2020 at 2:12 | comment | added | Jiachen Yuan | @AsafKaragila, I doubt it. Isn't it the case that such a forcing, let's say $P_\lambda$ always singularize some inaccessible $\theta$ which lives in between $\kappa$ and $\lambda$ to be of confinality $\omega$? | |
| Sep 2, 2020 at 15:07 | comment | added | Asaf Karagila♦ | Suppose that there is a Woodin cardinal above $\kappa$, can you do some tricks to ensure that the stationary tower will preserve the supercompactness? | |
| Sep 2, 2020 at 13:28 | history | asked | Jiachen Yuan | CC BY-SA 4.0 |