Timeline for Can the first ordinal in which $V\neq HOD$ be $\aleph_\omega$?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 22, 2015 at 7:59 | vote | accept | Yair Hayut | ||
| Oct 19, 2015 at 7:08 | answer | added | Mohammad Golshani | timeline score: 9 | |
| Mar 31, 2015 at 16:57 | comment | added | Yair Hayut | @MohammadGolshani: You can code the intermediate generic into the continuum function far above the strong cardinal in order to force $HOD$ to include it. This would not affect the homogeneity of the quotient forcing (I still don't see why the quotient is homogeneous). | |
| Mar 31, 2015 at 9:59 | comment | added | Yair Hayut | @MohammadGolshani: Please post an answer. There are still some details that I don't understand. If I understand correctly, you say that you can perform this forcing with only one measurable, right? | |
| Mar 31, 2015 at 7:56 | comment | added | Asaf Karagila♦ | @Mohammad: I thought that for a weakly homogeneous $HOD^{V[G]}\subseteq HOD(\Bbb P)^V$. So you need to have $HOD(\Bbb P)=HOD$. Which is indeed the case for $L[\mu]$. | |
| Mar 31, 2015 at 7:46 | comment | added | Mohammad Golshani | @AsafKaragila The forcing is definable at least in intermediate submodel, and that's enough. | |
| Mar 31, 2015 at 7:45 | comment | added | Yair Hayut | @MohammadGolshani: I'll take a look at these papers. Thank you. | |
| Mar 31, 2015 at 7:41 | comment | added | Asaf Karagila♦ | I think that you also need to have that the Prikry forcing is definable in $L[\mu]$, not just weakly homogeneous. | |
| Mar 31, 2015 at 7:28 | comment | added | Yair Hayut | @MohammadGolshani: It sounds good. Can you describe the tail forcing? Why is it homogeneous in the intermediate model? | |
| Mar 31, 2015 at 6:54 | history | asked | Yair Hayut | CC BY-SA 3.0 |