Timeline for Interesting meta-meta-mathematical theorems?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 21, 2021 at 19:38 | comment | added | Bjørn Kjos-Hanssen | OK, sure $\, \, \, \, \, $ | |
| Apr 21, 2021 at 19:28 | comment | added | Vladimir Reshetnikov | Yes, that version makes sense. But there are subtle issues with those definitions: the outcome depends on which exact representation for each recursive ordinal you choose at each step. See mathoverflow.net/q/67214/9550, mathoverflow.net/a/171723/9550. | |
| Apr 21, 2021 at 19:17 | comment | added | Bjørn Kjos-Hanssen | Ah... I guess I meant something like T_1= ZFC+Con ZFC, then T_2 = T_1+Con T_1 ... | |
| Apr 21, 2021 at 18:35 | comment | added | Vladimir Reshetnikov | Does ${\sf ZFC}\not\vdash\alpha_n$ represent “${\sf ZFC}$ cannot prove $\alpha_n$”? If so, then $\alpha_1$ represents “${\sf ZFC}$ cannot prove $\operatorname{Con}\left({\sf ZFC}\right)$”, right? Isn’t this statement logically equivalent in ${\sf ZFC}$ (or even ${\sf PA}$) to just $\operatorname{Con}\left({\sf ZFC}\right)$, i.e. $\alpha_0$? And, hence, all $\alpha_\beta$ are equivalent to $\alpha_0$ as well, no? | |
| Mar 8, 2014 at 16:31 | history | answered | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |