Difference between revisions of "Lower attic"
From Cantor's Attic
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* [[admissible]] ordinals and [[Church-Kleene#relativized Church-Kleene ordinal | relativized Church-Kleene $\omega_1^x$]] | * [[admissible]] ordinals and [[Church-Kleene#relativized Church-Kleene ordinal | relativized Church-Kleene $\omega_1^x$]] | ||
* [[Church-Kleene | Church-Kleene $\omega_1^{ck}$]], the supremum of the computable ordinals | * [[Church-Kleene | Church-Kleene $\omega_1^{ck}$]], the supremum of the computable ordinals | ||
| + | * the [[omega one chess | omega one of chess $\omega_1^{\rm chess}]] | ||
* the [[Feferman-Schütte]] ordinal [[Feferman-Schütte | $\Gamma_0$]] | * the [[Feferman-Schütte]] ordinal [[Feferman-Schütte | $\Gamma_0$]] | ||
* [[epsilon naught | $\epsilon_0$]] and the hierarchy of [[epsilon naught#epsilon_numbers | $\epsilon_\alpha$ numbers]] | * [[epsilon naught | $\epsilon_0$]] and the hierarchy of [[epsilon naught#epsilon_numbers | $\epsilon_\alpha$ numbers]] | ||
Revision as of 08:17, 30 December 2011
Welcome to the lower attic, where the countably infinite ordinals climb ever higher, one upon another, in an eternal self-similar reflecting ascent.
- $\omega_1$, the first uncountable ordinal, and the other uncountable cardinals of the middle attic
- stable ordinals
- The ordinals of infinite time Turing machines, including
- the Bachmann-Howard ordinal
- admissible ordinals and relativized Church-Kleene $\omega_1^x$
- Church-Kleene $\omega_1^{ck}$, the supremum of the computable ordinals
- the omega one of chess $\omega_1^{\rm chess}]] * the [[Feferman-Schütte]] ordinal [[Feferman-Schütte | $\Gamma_0$]] * [[epsilon naught | $\epsilon_0$]] and the hierarchy of [[epsilon naught#epsilon_numbers | $\epsilon_\alpha$ numbers]] * the [[small countable ordinals]], such as [[small countable ordinals | $\omega,\omega+1,\ldots,\omega\cdot 2,\ldots,\omega^2,\ldots,\omega^\omega,\ldots,\omega^{\omega^\omega},\ldots$]] up to [[epsilon naught | $\epsilon_0$]] * [[Hilberts hotel | Hilbert's hotel]] * [[omega | $\omega$, the smallest infinity
- down to the parlour, where large finite numbers dream
