Difference between revisions of "Lower 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 one chess|$\omega_1^{\mathfrak{Ch}_{\!\!\!\!\sim}}$]] = the supremum of the game values for white of all positions in infinite chess
 +
** [[omega one chess| $\omega_1^{\mathfrak{Ch},c}$]] = the supremum of the game values for white of the computable positions in infinite chess
 +
** [[omega one chess| $\omega_1^{\mathfrak{Ch}}$]] = the supremum of the game values for white of the finite positions in infinite chess
 
* the [[Madore's ψ function#Bachmann-Howard ordinal|Bachmann-Howard]] ordinal
 
* the [[Madore's ψ function#Bachmann-Howard ordinal|Bachmann-Howard]] ordinal
 
* the [[large Veblen]] ordinal
 
* the [[large Veblen]] ordinal
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* 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|$\omega_1^{\mathfrak{Ch}_{\!\!\!\!\sim}}$]] = the supremum of the game values for white of all positions in infinite chess
 
** [[omega one chess| $\omega_1^{\mathfrak{Ch},c}$]] = the supremum of the game values for white of the computable positions in infinite chess
 
** [[omega one chess| $\omega_1^{\mathfrak{Ch}}$]] = the supremum of the game values for white of the finite positions in infinite 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 | $\epsilon_0$]]  

Revision as of 22:03, 28 January 2017

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.