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]] <!--(ZFC without powerset axiom) is much above $\Sigma_n$-admissible, much below ZFC (stable ordinals as part of ZFC have no consistency strength)-->
+
* [[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)-->
 
* 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,

Revision as of 17:21, 22 September 2021

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.