Difference between revisions of "Lower attic"
From Cantor's Attic
| Line 7: | Line 7: | ||
* [[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_numbers | $\epsilon_1$]] and the [[epsilon naught#epsilon_numbers | $\epsilon_\alpha$ hierarchy]] |
| − | * [[ | + | * [[epsilon naught | $\epsilon_0$]] |
| − | * the [[small countable ordinals]], those below [[ | + | * the [[small countable ordinals]], those below [[epsilon naught | $\epsilon_0$]] |
* [[Hilberts hotel | Hilbert's hotel]] | * [[Hilberts hotel | Hilbert's hotel]] | ||
* [[<math>\omega</math>]] | * [[<math>\omega</math>]] | ||
Revision as of 21:19, 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
- [[\(\omega\)]]
