Lower 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

• The ordinals of infinite time Turing machines, including
  • $\Sigma$ = the supremum of the accidentally writable ordinals
  • $\zeta$ = the supremum of the eventually writable ordinals
  • $\lambda$ = the supremum of the writable ordinals,
• $\omega_1^x$
• 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
• $\omega$