Timeline for Fat stationary sets
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Jan 30, 2017 at 16:06 | history | edited | saf | CC BY-SA 3.0 |
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| Apr 9, 2016 at 18:07 | vote | accept | Monroe Eskew | ||
| Apr 8, 2016 at 14:44 | comment | added | Asaf Karagila♦ | @Monroe: That's pretty cool, then. I hope that all in all the fact you can always force it with a "nice" forcing (in the two cases, that is) is sufficient to solve your problem. | |
| Apr 8, 2016 at 14:26 | comment | added | Monroe Eskew | @AsafKaragila I think I have a way of forcing this with a $\lambda^+$-closed forcing. This cannot introduce $\square_lambda$. | |
| Apr 8, 2016 at 10:00 | comment | added | Asaf Karagila♦ | Duh, of course. :-) But can you force one without forcing a square sequence? | |
| Apr 8, 2016 at 10:00 | comment | added | saf | Just force square. | |
| Apr 8, 2016 at 9:45 | comment | added | Asaf Karagila♦ | A fat partition. | |
| Apr 8, 2016 at 9:36 | comment | added | saf | @asaf Force what? | |
| Apr 8, 2016 at 9:16 | comment | added | Asaf Karagila♦ | Can you at least force something like this at a successor of singular, like you can with an inaccessible? | |
| Apr 8, 2016 at 7:07 | history | edited | saf | CC BY-SA 3.0 |
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| Apr 8, 2016 at 6:35 | history | edited | saf | CC BY-SA 3.0 |
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| Apr 8, 2016 at 6:27 | history | edited | saf | CC BY-SA 3.0 |
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| Apr 8, 2016 at 6:08 | comment | added | Asaf Karagila♦ | Okay, so we're back to square one. Pun semi intended. | |
| Apr 8, 2016 at 5:50 | comment | added | saf | Correction: I just realized that MM implies the existence of $\aleph_2$ many pairwise disjoint fat subsets of $\aleph_2$. | |
| Apr 8, 2016 at 5:42 | comment | added | Asaf Karagila♦ | But usually $\omega_2$ is not a successor of singular. At least when assuming MM. :-) | |
| Apr 8, 2016 at 5:41 | comment | added | saf | Under Martin's Maximum, there cannot be two disjoint fat stationary subsets of $\omega_2$. | |
| Apr 8, 2016 at 5:26 | comment | added | Asaf Karagila♦ | Yes, but can you show that it is consistent without square that no such partition exists? | |
| Apr 8, 2016 at 5:14 | comment | added | saf | @asaf For Clause (1)? I just need a $\square(\lambda^+)$ sequence for which $\{ \alpha<\lambda^+\mid \text{otp}(C_\alpha)\ge\lambda\}$ is stationary. | |
| Apr 8, 2016 at 4:31 | comment | added | Asaf Karagila♦ | How necessary is the square? | |
| Apr 8, 2016 at 4:19 | history | answered | saf | CC BY-SA 3.0 |