Timeline for Is it consistent that the gaps between cardinals $\kappa$ and $2^\kappa$ "get larger and larger"?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| May 10, 2016 at 11:40 | comment | added | Joel David Hamkins | @AsafKaragila If you notice how Dominic had asked his question, he inquires not just that there are arbitrarily large gaps, but that the gaps become eventually as large as desired, and so this would include singular cardinals. So I think we really need the sophisticated tools of the Foreman-Woodin model. | |
| May 10, 2016 at 11:30 | vote | accept | Dominic van der Zypen | ||
| May 10, 2016 at 11:28 | answer | added | Mohammad Golshani | timeline score: 5 | |
| May 10, 2016 at 10:39 | comment | added | Asaf Karagila♦ | @Gro-Tsen: Of course it will give the answer. Even if you only apply Easton's theorem to the class of successors of limits of cofinality $\omega$, it will still suffice to ensure the gaps are arbitrarily large. | |
| May 10, 2016 at 9:04 | comment | added | Gro-Tsen | @DavidRoberts Will it? The question includes those $\lambda$ for which $\aleph_\lambda$ is singular, and unlike regular cardinals, those are not an easy matter to control. I seem to remember a past question on the consistency of $(\forall\lambda)\,2^{\aleph_\lambda}=\aleph_{\lambda+2}$, and while I can't remember the conclusion, I think it wasn't at all trivial. | |
| May 10, 2016 at 8:33 | comment | added | David Roberts♦ | Easton's theorem will give you the answer, methinks | |
| May 10, 2016 at 7:13 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |