Timeline for Incompleteness theorems for theories with omega-rule
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 15, 2020 at 1:51 | comment | added | BPP | Yes, that's exactly it. Where can I read up on the proof of this? | |
| Oct 14, 2020 at 21:11 | comment | added | BPP | A related question that's in the spirit of the previous question is, is there a version of the incompleteness theorem for set theory that guarantees an independent sentence for any theory, but with the proviso that this independent sentence has no arithmetic consequences (like CH or AC relative to ZF)? | |
| Oct 14, 2020 at 20:00 | vote | accept | BPP | ||
| Oct 14, 2020 at 18:41 | comment | added | Emil Jeřábek | I don’t really know, but I suspect that stuff will break in various ways when you move to uncountable analogues of the $\omega$-rule. (In general, $L_{\omega_1,\omega}$, of which the $\omega$-rule can be seen as a special case, is much more well behaved that $L_{\kappa,\omega}$ for $\kappa>\omega_1$.) | |
| Oct 14, 2020 at 18:16 | comment | added | BPP | Thanks. Do similar phenomena arise when we add the stronger generalizations of the omega-rule to set theories stronger than analysis? And is there any rule analogous to the omega-rule that makes all sentences of analysis provable or refutable? | |
| Oct 14, 2020 at 16:53 | history | answered | Emil Jeřábek | CC BY-SA 4.0 |