Difference between revisions of "Lower attic"
From Cantor's Attic
| Line 10: | Line 10: | ||
* [[admissible]] ordinals | * [[admissible]] ordinals | ||
* [[Gamma | $\Gamma$]] | * [[Gamma | $\Gamma$]] | ||
| − | * Church-Kleene [[Church-Kleene omega_1 | $\omega_1^{ck}$]] | + | * Church-Kleene [[Church-Kleene omega_1 | $\omega_1^{ck}$]], the supremum of the computable ordinals |
* [[epsilon naught | $\epsilon_0$]] and the hierarchy of [[epsilon naught#epsilon_numbers | $\epsilon_\alpha$ numbers]] | * [[epsilon naught | $\epsilon_0$]] and the hierarchy of [[epsilon naught#epsilon_numbers | $\epsilon_\alpha$ numbers]] | ||
* the [[small countable ordinals]], those below [[epsilon naught | $\epsilon_0$]] | * the [[small countable ordinals]], those below [[epsilon naught | $\epsilon_0$]] | ||
* [[Hilberts hotel | Hilbert's hotel]] | * [[Hilberts hotel | Hilbert's hotel]] | ||
* [[omega | $\omega$]] | * [[omega | $\omega$]] | ||
Revision as of 21:37, 27 December 2011
Welcome to the lower attic, where we store the comparatively smaller notions of infinity. Roughly speaking, this is the realm of countable ordinals and their friends.
- Up to The middle attic
- The ordinals of infinite time Turing machines, including
- $\omega_1^x$
- admissible ordinals
- $\Gamma$
- Church-Kleene $\omega_1^{ck}$, the supremum of the computable ordinals
- $\epsilon_0$ and the hierarchy of $\epsilon_\alpha$ numbers
- the small countable ordinals, those below $\epsilon_0$
- Hilbert's hotel
- $\omega$
