# Difference between revisions of "Lower attic"

From Cantor's Attic

Line 11: | Line 11: | ||

* [[Gamma | $\Gamma$]] | * [[Gamma | $\Gamma$]] | ||

* Church-Kleene [[Church-Kleene omega_1 | $\omega_1^{ck}$]] | * Church-Kleene [[Church-Kleene omega_1 | $\omega_1^{ck}$]] | ||

− | * [[epsilon naught | + | * [[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 21:29, 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 $\omega_1^{ck}$
- $\epsilon_0$ and the hierarchy of $\epsilon_\alpha$ numbers
- the small countable ordinals, those below $\epsilon_0$
- Hilbert's hotel
- $\omega$