Difference between revisions of "Upper attic"

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(Changed Vopenka links to match Vopenka page)
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* [[Mahlo]] cardinal
 
* [[Mahlo]] cardinal
 
* [[ORD is Mahlo]]
 
* [[ORD is Mahlo]]
* [[reflecting#Inaccessible reflecting cardinal | inaccessible $\Sigma_2$-reflecting]], [[reflecting#Inaccessible reflecting cardinal | inaccessible $\Sigma_n$-reflecting]] and [[reflecting#Inaccessible reflecting cardinal| inaccessible reflecting]] cardinals
+
* [[reflecting#$\Sigma_2$ reflecting cardinal | $\Sigma_2$-reflecting]], [[reflecting | $\Sigma_n$-reflecting]] and [[reflecting]] cardinals
 
* [[inaccessible#Degrees of inaccessibility | $1$-inaccessible]], the [[inaccessible#Degrees of inaccessibility | $\alpha$-inaccessible]] hierarchy and  [[inaccessible#Hyper-inaccessible | hyper-inaccessible]] cardinals
 
* [[inaccessible#Degrees of inaccessibility | $1$-inaccessible]], the [[inaccessible#Degrees of inaccessibility | $\alpha$-inaccessible]] hierarchy and  [[inaccessible#Hyper-inaccessible | hyper-inaccessible]] cardinals
 
* [[inaccessible#Universes | Grothendieck universe axiom]], equivalent to the existence of a proper class of [[inaccessible]] cardinals
 
* [[inaccessible#Universes | Grothendieck universe axiom]], equivalent to the existence of a proper class of [[inaccessible]] cardinals
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* the [[Transitive ZFC model#Minimal transitive model of ZFC | minimal transitive model]]
 
* the [[Transitive ZFC model#Minimal transitive model of ZFC | minimal transitive model]]
 
* [[Con ZFC | Con(ZFC)]] and [[Con ZFC#Consistency hierarchy | $\text{Con}^\alpha(\text{ZFC})$]], the [[Con ZFC#Consistency hierarchy | iterated consistency hierarchy]]  
 
* [[Con ZFC | Con(ZFC)]] and [[Con ZFC#Consistency hierarchy | $\text{Con}^\alpha(\text{ZFC})$]], the [[Con ZFC#Consistency hierarchy | iterated consistency hierarchy]]  
 +
* [[correct]] cardinal
  
 
* down to [[the middle attic]]
 
* down to [[the middle attic]]

Revision as of 18:39, 22 July 2013

Cape Pogue Lighthouse photo by Timothy Valentine

Welcome to the upper attic, the transfinite realm of large cardinals, the higher infinite, carrying us upward from the merely inaccessible and indescribable to the subtle and endlessly extendible concepts beyond, towards the calamity of inconsistency.