# Lower attic

From Cantor's Attic

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
- [[\(\omega\)]]