Timeline for Removing large cardinals from an uncountable transitive model
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 9, 2015 at 12:35 | answer | added | Grigor | timeline score: 4 | |
| Nov 17, 2015 at 21:00 | vote | accept | Miha Habič | ||
| Nov 17, 2015 at 1:36 | answer | added | Trevor Wilson | timeline score: 18 | |
| Nov 11, 2015 at 15:23 | comment | added | Asaf Karagila♦ | Yeah, I meant of course the latter case. How about trying to show that in that situation there is no uncountable model without an inaccessible? | |
| Nov 11, 2015 at 14:57 | comment | added | Miha Habič | @AsafKaragila Well, that will give you an uncountable model with lots of inaccessibles. One would then have to argue that there are also models which are quite far from $L$, where all of the inaccessibles have been killed. This is simple enough to do if we additionally assume that in $L$ there is a transitive model containing $L_{\kappa+1}$ (where $\kappa$ is the Mahlo), but if there isn't I am not sure how to proceed. | |
| Nov 11, 2015 at 9:02 | comment | added | Asaf Karagila♦ | My usual solution when I'm stuck is to try and engineer a counterexample. Have you tried starting with $L$ with a single Mahlo and collapse it to be $\omega_1$? | |
| Nov 11, 2015 at 5:46 | history | asked | Miha Habič | CC BY-SA 3.0 |