Difference between revisions of "Lower attic"

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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.  
 
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.  
  
* [[aleph_1 | $\omega_1$]], the first uncountable ordinal, and the other uncountable cardinals of the [[middle attic]]
+
* $\ursh$ [[aleph_1 | $\omega_1$]], the first uncountable ordinal, and the other uncountable cardinals of the [[middle attic]]
 
* 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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* [[Hilberts hotel | Hilbert's hotel]]
 
* [[Hilberts hotel | Hilbert's hotel]]
 
* [[omega | $\omega$]], the smallest infinity
 
* [[omega | $\omega$]], the smallest infinity
* down to the [[subattic]], containing very large finite numbers
+
* $\drsh$ to the [[subattic]], containing very large finite numbers

Revision as of 09:18, 28 December 2011

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.