Difference between revisions of "Lower attic"

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(the Takeuti-Feferman-Buchholz ordinal)
(ZFC-P<!--much above, much below...-->)
Line 7: Line 7:
 
*  [[aleph one | $\omega_1$]], the first uncountable ordinal, and the other uncountable cardinals of the [[middle attic]]
 
*  [[aleph one | $\omega_1$]], the first uncountable ordinal, and the other uncountable cardinals of the [[middle attic]]
 
* [[stable]] ordinals
 
* [[stable]] ordinals
 +
* models of [[ZFC-P]] (ZFC without powerset axiom)<!--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 11:03, 15 November 2019

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.