Timeline for Absoluteness of well-orderability
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 12, 2023 at 8:03 | vote | accept | Adam Epstein | ||
| Oct 20, 2022 at 14:19 | comment | added | Julia Williams | Ah that explains why this argument seemed so familiar to me! | |
| Oct 19, 2022 at 16:17 | comment | added | Noah Schweber | Related: mathoverflow.net/questions/236041/… | |
| Oct 19, 2022 at 14:54 | answer | added | Julia Williams | timeline score: 10 | |
| Jun 10, 2018 at 7:26 | history | edited | Adam Epstein | CC BY-SA 4.0 |
added 6 characters in body
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| Jun 7, 2018 at 20:12 | comment | added | Adam Epstein | And very much like Boffa's example discussed here mathoverflow.net/questions/85941/… | |
| Jun 7, 2018 at 19:35 | comment | added | Philip Welch | @StefanMesken: there is an r.e. linear ordering, $R$, of $\omega$, which is thus in $M= L_{\omega_1^{ck}}$, but there are no infinite descending chains through $R$ in $M$. (The wellordered part of $R$ has order type ${\omega_1^{ck}}$ but there is an illfounded part beyond it.). This is exactly as Asaf puts it: we move beyond $M$ and can then find a set which witnesses the illfoundedness of $R$. (The existence of such an $R$: R.O. Gandy: A proof of Mostowski's Conjecture (1960).) | |
| Jun 7, 2018 at 15:02 | comment | added | Adam Epstein | @AsafKaragila Thank you so much! This came to mind several months ago when I was mentally verifying some assertion in whatever I was reading at the time (I think a paper of Joel's). I felt I'd really learned something. | |
| Jun 7, 2018 at 14:38 | comment | added | Asaf Karagila♦ | I like this question. On first sight, it seems like the answer is "obviously yeah", but then you realize that moving to a larger model, one might have added a new set which witnesses the ill-foundedness. Nice! | |
| Jun 7, 2018 at 12:52 | comment | added | Stefan Mesken | @PhilipWelch Could you elaborate on the illfounded ordering of $L_{\omega_1^{ck}}$? I'm not sure where it comes from. | |
| Jun 7, 2018 at 9:43 | comment | added | Philip Welch | Upwards absoluteness of WO's fails for transitive models of KP (so Pairing, Union, Inf., Found, with Delta_1-Sep. and Sigma_1-Rep.). This is witnessed by an illfounded ordering in the least transitive KP model: L_{omega_1}^{ck}. But if Sigma_1 Rep. is enhanced to Sigma_2-Rep, then the transitive models here are "beta-models": \Pi^1_1 statements, including thus Wellordering, are absolute between them and V. | |
| Jun 7, 2018 at 8:30 | history | asked | Adam Epstein | CC BY-SA 4.0 |