Difference between revisions of "Lower attic"
From Cantor's Attic
| Line 3: | Line 3: | ||
* Up to [[The middle attic]] | * Up to [[The middle attic]] | ||
| − | * The ordinals of [[infinite time Turing machines]], | + | * The ordinals of [[infinite time Turing machines]], including |
| − | ** [[infinite time Turing machines#Sigma | $\Sigma$]] | + | ** [[infinite time Turing machines#Sigma | $\Sigma$]] = the supremum of the accidentally writable ordinals |
| − | ** [[infinite time Turing machines#zeta | $\zeta$]] | + | ** [[infinite time Turing machines#zeta | $\zeta$]] = the supremum of the eventually writable ordinals |
| − | ** [[infinite time Turing machines#lambda | $\lambda$]] | + | ** [[infinite time Turing machines#lambda | $\lambda$]] = the supremum of the writable ordinals, |
* [[admissible#relativized_admissible | $\omega_1^x$]] | * [[admissible#relativized_admissible | $\omega_1^x$]] | ||
* [[admissible]] ordinals | * [[admissible]] ordinals | ||
Revision as of 21:27, 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 $\omega_1^{ck}$
- $\epsilon_1$ and the $\epsilon_\alpha$ hierarchy
- $\epsilon_0$
- the small countable ordinals, those below $\epsilon_0$
- Hilbert's hotel
- $\omega$
