Timeline for A set for which it is hard to determine whether or not it is countable.
Current License: CC BY-SA 2.5
5 events
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| Mar 23, 2011 at 11:59 | comment | added | Bjørn Kjos-Hanssen | @Tanmay: apparently they show NCR$_n$ is properly $\mathbf\Pi^1_1$ as soon as there are not enough power sets (and countable hence $\mathbf\Sigma^0_2$ when there are). | |
| Mar 22, 2011 at 17:10 | comment | added | KConrad | This example is missing the condition in the statement of the problem that any graduate student can think about it, although I'll grant you that they'd still not have an answer after 10 minutes. | |
| Mar 22, 2011 at 14:16 | comment | added | user3462 | So, depending on how many iterates you have, you can go from $\Pi_{1}^{1}\setminus\Delta_{1}^{1}$ to $\Sigma_{2}^{0}$? (Wow!) | |
| Mar 22, 2011 at 12:57 | comment | added | user3462 | Bjørn, does the Borel rank of the NCR$_n$ change depending on how many iterates of the power set of the natural numbers are assumed? | |
| Mar 22, 2011 at 2:14 | history | answered | Bjørn Kjos-Hanssen | CC BY-SA 2.5 |