# Difference between revisions of "Lower attic"

From Cantor's Attic

Line 6: | Line 6: | ||

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

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

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

* [[epsilon0#epsilon_numbers | $\epsilon_1$]] and the [[epsilon0#epsilon_numbers | $\epsilon_\alpha$ hierarchy]] | * [[epsilon0#epsilon_numbers | $\epsilon_1$]] and the [[epsilon0#epsilon_numbers | $\epsilon_\alpha$ hierarchy]] | ||

* [[epsilon0 | $\epsilon_0$]] | * [[epsilon0 | $\epsilon_0$]] |

## Revision as of 21:17, 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

- $\omega_1^x$
- 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
- [[\(\omega\)]]