# Difference between revisions of "Lower attic"

From Cantor's Attic

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* Up to [[The middle attic]] | * Up to [[The middle attic]] | ||

− | * $\omega_1^x$ | + | |

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

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

− | * $\Gamma$ | + | * [[Gamma | $\Gamma$]] |

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

− | * | + | * [epsilon0#epsilon_alpha | the $\epsilon_\alpha$ hierarchy]] |

− | * $\epsilon_1$ | + | * [[epsilon0#epsilon_1 | $\epsilon_1$]] |

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

* Ordinals below $\omega^\omega$ | * Ordinals below $\omega^\omega$ | ||

− | + | * [[small countable ordinals | small countably infinite ordinals]] | |

− | + | * [[Hilberts hotel | Hilbert's hotel]] | |

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | * [[ | + | |

− | * [[Hilbert' hotel]] | + | |

* [[<math>\omega</math>]] | * [[<math>\omega</math>]] |

## Revision as of 20:52, 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
- $\Gamma$
- $\omega_1^{ck}$
- [epsilon0#epsilon_alpha | the $\epsilon_\alpha$ hierarchy]]
- $\epsilon_1$
- $\epsilon_0$
- Ordinals below $\omega^\omega$
- small countably infinite ordinals
- Hilbert's hotel
- [[\(\omega\)]]