Difference between revisions of "Lower attic"

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(the Takeuti-Feferman-Buchholz ordinal)
 
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{{DISPLAYTITLE: The lower attic}}
 
{{DISPLAYTITLE: The lower attic}}
 
[[File:SagradaSpiralByDavidNikonvscanon.jpg | thumb | Sagrada Spiral photo by David Nikonvscanon]]
 
[[File:SagradaSpiralByDavidNikonvscanon.jpg | thumb | Sagrada Spiral photo by David Nikonvscanon]]
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[[Category:Lower attic]]
  
 
Welcome to the lower attic, where the countably infinite ordinals climb ever higher, one upon another, in an eternal self-similar reflecting ascent.
 
Welcome to the lower attic, where the countably infinite ordinals climb ever higher, one upon another, in an eternal self-similar reflecting ascent.
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** [[infinite time Turing machines#zeta | $\zeta$]] = the supremum of the eventually writable ordinals  
 
** [[infinite time Turing machines#zeta | $\zeta$]] = the supremum of the eventually writable ordinals  
 
** [[infinite time Turing machines#lambda | $\lambda$]] = the supremum of the writable ordinals,  
 
** [[infinite time Turing machines#lambda | $\lambda$]] = the supremum of the writable ordinals,  
* the [[Bachmann-Howard]] ordinal
 
 
* [[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
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* the [[omega one chess | omega one of chess]]
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** [[omega one chess|$\omega_1^{\mathfrak{Ch}_{\!\!\!\!\sim}}$]] = the supremum of the game values for white of all positions in infinite chess
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** [[omega one chess| $\omega_1^{\mathfrak{Ch},c}$]] = the supremum of the game values for white of the computable positions in infinite chess
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** [[omega one chess| $\omega_1^{\mathfrak{Ch}}$]] = the supremum of the game values for white of the finite positions in infinite chess
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* the [[Buchholz's ψ functions#Takeuti-Feferman-Buchholz ordinal|Takeuti-Feferman-Buchholz]] ordinal
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* the [[Madore's ψ function#Bachmann-Howard ordinal|Bachmann-Howard]] ordinal
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* the [[Madore's ψ function#Large Veblen ordinal|large Veblen]] ordinal
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* the [[Madore's ψ function#Small Veblen ordinal|small Veblen]] ordinal
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* the [[Extended Veblen function]]
 
* 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]]
* the [[omega one chess | omega one of chess]], [[omega one chess| $\omega_1^{\rm chess}$]]
 
 
* [[indecomposable]] ordinal
 
* [[indecomposable]] ordinal
 
* 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 | $\epsilon_0$]]  
 
* 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 | $\epsilon_0$]]  

Latest revision as of 13:37, 27 May 2018

Sagrada Spiral photo by David Nikonvscanon

Welcome to the lower attic, where the countably infinite ordinals climb ever higher, one upon another, in an eternal self-similar reflecting ascent.