Difference between revisions of "Lower attic"

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[[File:SagradaSpiralByDavidNikonvscanon.jpg | right | Sagrada Spiral photo by David Nikonvscanon]]
 
[[File:SagradaSpiralByDavidNikonvscanon.jpg | right | Sagrada Spiral photo by David Nikonvscanon]]
  
Welcome to the lower attic, where we store the comparatively smaller notions of infinity. Roughly speaking, this is the realm of countable ordinals and their friends.  
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Welcome to the lower attic, where the countably infinite ordinals climb ever higher, one upon another, in an endlessly self-similar reflecting ascent, whose life-giving everlasting beauty enraptures us.
 
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*  [[aleph_1 | $\omega_1$]], the first uncountable ordinal, and the other uncountable cardinals of the [[middle attic]]
 
*  [[aleph_1 | $\omega_1$]], the first uncountable ordinal, and the other uncountable cardinals of the [[middle attic]]
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* [[admissible#relativized_admissible | $\omega_1^x$]]
 
* [[admissible#relativized_admissible | $\omega_1^x$]]
 
* [[admissible]] ordinals
 
* [[admissible]] ordinals
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* Church-Kleene [[Church-Kleene omega_1 | $\omega_1^{ck}$]], the supremum of the computable ordinals
 
* [[Gamma | $\Gamma$]]
 
* [[Gamma | $\Gamma$]]
* Church-Kleene [[Church-Kleene omega_1 | $\omega_1^{ck}$]], the supremum of the computable ordinals
 
 
* [[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 [[small countable ordinals]], those below [[epsilon naught | $\epsilon_0$]]  
 
* the [[small countable ordinals]], those below [[epsilon naught | $\epsilon_0$]]  

Revision as of 20:24, 28 December 2011

Sagrada Spiral photo by David Nikonvscanon

Welcome to the lower attic, where the countably infinite ordinals climb ever higher, one upon another, in an endlessly self-similar reflecting ascent, whose life-giving everlasting beauty enraptures us.