Timeline for Woodin's unpublished proof of the global failure of GCH
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 3, 2013 at 3:31 | answer | added | Mohammad Golshani | timeline score: 9 | |
| Aug 2, 2013 at 1:08 | answer | added | Andrés E. Caicedo | timeline score: 13 | |
| Aug 2, 2013 at 0:40 | comment | added | Andrés E. Caicedo | (I'm turning my comments into an answer.) | |
| Aug 1, 2013 at 14:33 | comment | added | Ramiro de la Vega | @Andres: why a comment and not an answer? | |
| Aug 1, 2013 at 14:21 | comment | added | Andrés E. Caicedo | His argument assumes $\mathsf{GCH}$ and that $\kappa$ is what is either called $\kappa+n$-strong or $\kappa^{+n+1}$-strong, that is, there is $j:V\to M$ with $\mathrm{cp}(j)=\kappa$ and $V_{\kappa+n}\subset M$. His assumptions are an overkill, since in the final model he preserves inaccessibility of $\kappa$, and $V_\kappa$ is the model where $\forall \lambda,(2^\lambda=\lambda^{+n})$. | |
| Aug 1, 2013 at 14:15 | comment | added | Andrés E. Caicedo | As you say, Hugh's precise result is unpublished (it does not use the supercompact version of Radin's forcing, but what you call the ordinary version). The only published full account of the result that I can think of currently is Carmi Merimovich. A Power Function with a Fixed Finite Gap Everywhere, The Journal of Symbolic Logic, 72 (2), (2007), 361-417. Merimovich uses extender based Radin forcing, his argument can give $\forall\lambda\,(2^\lambda=\lambda^{+n})$ for any fixed $n$, $1<n<\omega$, though he presents the details for $n=3$. | |
| Aug 1, 2013 at 13:07 | comment | added | Péter Komjáth | My understanding is that Foreman-Woodin: $\forall\lambda, 2^\lambda\geq\lambda^{++}$, Woodin, later: $\forall\lambda, 2^\lambda=\lambda^{++}$. | |
| Aug 1, 2013 at 13:00 | comment | added | Joel David Hamkins | Isn't the result due to Foreman and Woodin? Also, see mathoverflow.net/questions/79920/failure-of-the-gch. | |
| Aug 1, 2013 at 9:30 | history | asked | Mohammad Golshani | CC BY-SA 3.0 |