Timeline for What is $\omega_1^{CK}(\mathsf{Ord})$?
Current License: CC BY-SA 3.0
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| Dec 18, 2012 at 14:48 | comment | added | Andreas Blass | As far as I can see, the next admissible set remains an upper bound, no matter what large-cardinal axioms $M$ satisfies. What that next admissible set is depends, of course, on $M$, and I'd expect it may depend on other things than just large-cardinal properties. | |
| Dec 17, 2012 at 21:31 | comment | added | Asaf Karagila♦ | Also you are spot on the first-order definable [with parameters] over $M$. I borrowed the notation because I found it somewhat relevant, $\omega_1^{CK}$ is the $\omega_1^{CK}(\mathsf{Ord}^{V_\omega})$ of the theory ZFC-Infinity+$\lnot$Infinity. | |
| Dec 17, 2012 at 18:38 | comment | added | Asaf Karagila♦ | Thanks Andreas, is there anything large cardinals can do to affect the outcome? For example if $M\models\exists 0^\#$, or has a proper class of superhuge cardinals? I suppose that from that we can define more orderings... | |
| Dec 17, 2012 at 15:15 | history | answered | Andreas Blass | CC BY-SA 3.0 |