Difference between revisions of "Lower attic"

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*  [[Aleph#Aleph_one| $\omega_1$]], the first uncountable ordinal, and the other uncountable cardinals of the [[middle attic]]
 
*  [[Aleph#Aleph_one| $\omega_1$]], the first uncountable ordinal, and the other uncountable cardinals of the [[middle attic]]
 
* [[stable]] ordinals
 
* [[stable]] ordinals
* [[Heights of models]], [[Skolem's paradox]] <!--(ZFC without powerset axiom) is much above $\Sigma_n$-admissible, much below ZFC (stable ordinals as part of ZFC have no consistency strength)-->
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* [[Heights of models]] <!--(ZFC without powerset axiom) is much above $\Sigma_n$-admissible, much below ZFC (stable ordinals as part of ZFC have no consistency strength)-->
 
* The ordinals of [[infinite time Turing machines]], including   
 
* The ordinals of [[infinite time Turing machines]], including   
 
** [[infinite time Turing machines#Sigma | $\Sigma$]] = the supremum of the accidentally writable ordinals,
 
** [[infinite time Turing machines#Sigma | $\Sigma$]] = the supremum of the accidentally writable ordinals,
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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  
 
** [[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
 
** [[omega one chess| $\omega_1^{\mathfrak{Ch}}$]] = the supremum of the game values for white of the finite positions in infinite chess
* the [[Buchholz's ψ functions#Takeuti-Feferman-Buchholz ordinal|Takeuti-Feferman-Buchholz]] ordinal
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* [[Buchholz's ψ functions]], the [[Buchholz's ψ functions#Takeuti-Feferman-Buchholz ordinal|Takeuti-Feferman-Buchholz]] ordinal
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* the [[RHS0]] notation
 
* the [[Madore's ψ function#Bachmann-Howard ordinal|Bachmann-Howard]] ordinal
 
* the [[Madore's ψ function#Bachmann-Howard ordinal|Bachmann-Howard]] ordinal
 
* the [[Madore's ψ function#Large Veblen ordinal|large Veblen]] ordinal
 
* the [[Madore's ψ function#Large Veblen ordinal|large Veblen]] ordinal

Latest revision as of 20:29, 1 July 2022

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.