Timeline for A question on the provability predicate of Q
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 17, 2016 at 17:01 | vote | accept | Frode Alfson Bjørdal | ||
| Mar 17, 2016 at 16:59 | comment | added | Frode Alfson Bjørdal | It would seem so. As Q is also $\Sigma^0_0$-complete, all of $\vdash\lnot 0Prov[G]$, $\vdash\lnot 1Prov[G]$, $\vdash\lnot 2Prov[G]$ etc. hold. So $\nvdash\exists x(xProv[G]$ and thus $\nvdash\lnot G $ follow by omega consistencey. | |
| Mar 17, 2016 at 15:45 | comment | added | Frode Alfson Bjørdal | Thanks! If "Robinson investigated Q precisely because Q is strong enough for the usual proof of the first incompleteness theorem to go through" does it not mean that we can infer "the thesishood of A from the thesishood of $Pr[A] and the omega-consistency of Q"? | |
| Mar 17, 2016 at 13:42 | history | answered | Carl Mummert | CC BY-SA 3.0 |