# 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]], such as [[infinite time Turing machines#lambda | $\lambda$]], the supremum of the writable ordinals, [[infinite time Turing machines#zeta | $\zeta$]], the supremum of the eventually writable ordinals and [[infinite time Turing machines#Sigma | $\Sigma$]], the supremum of the accidentally writable ordinals | ||

* [[admissible#relativized_admissible | $\omega_1^x$]] | * [[admissible#relativized_admissible | $\omega_1^x$]] | ||

* [[admissible]] ordinals | * [[admissible]] ordinals |

## Revision as of 21:26, 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, such as $\lambda$, the supremum of the writable ordinals, $\zeta$, the supremum of the eventually writable ordinals and $\Sigma$, the supremum of the accidentally writable ordinals
- $\omega_1^x$
- 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
- $\omega$