Timeline for Solutions to the Continuum Hypothesis
Current License: CC BY-SA 3.0
21 events
| when toggle format | what | by | license | comment | |
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| Sep 1, 2021 at 6:05 | comment | added | Martin Sleziak | The first link seems to be dead, here is a link to a Wayback Machine snapshot. | |
| Mar 27, 2018 at 23:05 | history | edited | Andrés E. Caicedo | CC BY-SA 3.0 |
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| Mar 27, 2018 at 19:46 | comment | added | Andrés E. Caicedo | @Joel Thanks. I am aware of this (see here), and I knew there was a post of mine where I was using the incorrect terminology, but could never find it. :-) I'll update a bit later. | |
| Mar 27, 2018 at 19:38 | comment | added | Joel David Hamkins | Regarding your remark about bi-interpretability, this is too strong. In fact, different set theories extending ZF are never bi-interpretable (see jdh.hamkins.org/…). But one can still make the point somewhat with mere mutual interpretations, a lesser notion. | |
| Feb 26, 2018 at 22:21 | history | edited | David Feldman | CC BY-SA 3.0 |
Fixed typo
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| Feb 26, 2018 at 22:13 | history | edited | David Feldman | CC BY-SA 3.0 |
grammar and style
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| May 14, 2017 at 9:12 | comment | added | ACL | My recollection of Dehornoy's talk at the Bourbaki Seminar is that it was absolutely fantastic! | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Mar 20, 2017 at 5:34 | comment | added | Gil Kalai | The link to Woodin's 2010 lecture was broken and I replaced it with a link to a lecture in 2016. | |
| Mar 20, 2017 at 5:32 | history | edited | Gil Kalai | CC BY-SA 3.0 |
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| Jul 7, 2014 at 19:46 | history | edited | Gil Kalai | CC BY-SA 3.0 |
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| Dec 29, 2010 at 21:48 | comment | added | Andrés E. Caicedo | @John: Many thanks for the link! I'll post it again in the answer to the "Completion of ZFC" question I linked to above. | |
| Dec 29, 2010 at 21:34 | comment | added | John Stillwell | There are slides of a talk by Woodin about Ultimate L at phil.upenn.edu/WSTPM/Woodin | |
| Nov 23, 2010 at 15:45 | comment | added | Andrés E. Caicedo | (3) It can be shown that it is $H(\delta_0^+)$-definable, where $\delta_0$ is the smallest Woodin of $V$. But the argument pro-not-CH went by a level by level analysis of the $H(\kappa)$-levels, and this jump (from ${\mathfrak c}$ to a Woodin) is too high to overlook. As far as I understand, this is the nature of the issue. | |
| Nov 23, 2010 at 15:42 | comment | added | Andrés E. Caicedo | (2) Woodin's local definability argument depended on this limitation of hod models. (I am not sure of the details here.) Grigor's analysis in the context of the core model induction (there are slides of a talk at Boise on his website, and I can email you his thesis, let me know) showed that these "local overlaps" are possible, and deduced as a corollary that "$AD_{\mathbb R}+\Theta$ regular has much lower consistency strength than expected. Grigor in fact has a very detailed analysis of hod models. Without the overlap limitation, the set of $\Omega$-validities ends up being harder to define. | |
| Nov 23, 2010 at 15:33 | comment | added | Andrés E. Caicedo | Hi Simon. I am not too certain of all the details; I believe that the issue is this: In the context of $AD^+$, say that $\alpha$ is a "local $\Theta$" if it is the $\Theta$ of a hod-model. Woodin had an argument showing that no such $\alpha$ could be overlapped by a strong cardinal. This put serious limitations on the strength of large cardinals that hod-models could contain. In particular, this was the reason why it was expected that "CH + there is an $\omega_1$-dense ideal on $\omega_1$" and "$AD_{\mathbb R}+\Theta$ regular" were expected to have really high consistency strength (continued) | |
| Nov 23, 2010 at 13:08 | comment | added | Simon Thomas | Could you give some more details about the connection with the recent work of Sargsyan? | |
| Nov 23, 2010 at 6:10 | history | edited | Andrés E. Caicedo | CC BY-SA 2.5 |
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| May 20, 2010 at 3:58 | history | edited | Andrés E. Caicedo | CC BY-SA 2.5 |
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| May 18, 2010 at 23:47 | comment | added | John Stillwell | Thanks very much for this answer, Andres. I had heard that Woodin proved an extremal property of CH, but I didn't know what it was. It is presumably your item (2). | |
| May 18, 2010 at 21:50 | history | answered | Andrés E. Caicedo | CC BY-SA 2.5 |