Difference between revisions of "Upper attic"

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* [[huge]] cardinal
 
* [[huge]] cardinal
 
* [[huge#Almost huge | almost huge]] cardinal
 
* [[huge#Almost huge | almost huge]] cardinal
 +
* [[Vopenka | Vopěnka]] cardinal, [[Vopenka#Vopěnka's principle | Vopěnka's principle]
 
* [[extendible]] cardinal
 
* [[extendible]] cardinal
 
* [[grand reflection]] cardinal
 
* [[grand reflection]] cardinal
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* [[strongly compact]] cardinal
 
* [[strongly compact]] cardinal
 
* [[nearly supercompact]] and [[nearly supercompact#Nearly strongly compact | nearly strongly compact]] cardinals
 
* [[nearly supercompact]] and [[nearly supercompact#Nearly strongly compact | nearly strongly compact]] cardinals
 +
* [[subcompact]] cardinal
 
* [[strong#Superstrong | superstrong]] cardinal
 
* [[strong#Superstrong | superstrong]] cardinal
 +
* [[Shelah]] cardinal
 
* [[Woodin]] cardinal
 
* [[Woodin]] cardinal
 
* [[strong]] cardinal
 
* [[strong]] cardinal
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* [[Ramsey#Weakly_Ramsey | weakly Ramsey]] cardinal
 
* [[Ramsey#Weakly_Ramsey | weakly Ramsey]] cardinal
 
* [[Ramsey#Iterably_Ramsey | iterably Ramsey]] cardinal
 
* [[Ramsey#Iterably_Ramsey | iterably Ramsey]] cardinal
* [[Ramsey]] cardinal  
+
* [[Ramsey]] cardinal
* [[subtle]] cardinal
+
* [[Rowbottom]] cardinal
 +
* [[Jónsson]] cardinal
 
* [[zero sharp | $0^\sharp$]]
 
* [[zero sharp | $0^\sharp$]]
 
* [[Erdos]] cardinal, [[Erdos | $\omega_1$-Erdos]] and the [[Erdos | $\alpha$-Erdos]] hierarchy
 
* [[Erdos]] cardinal, [[Erdos | $\omega_1$-Erdos]] and the [[Erdos | $\alpha$-Erdos]] hierarchy
 +
* [[remarkable]] cardinals
 
* [[ineffible]] cardinal
 
* [[ineffible]] cardinal
 +
* [[subtle]] cardinal
 +
* [[ethereal]] cardinal
 
* [[unfoldable]] cardinal, [[unfoldable#Strongly unfoldable | strongly unfoldable]] cardinal
 
* [[unfoldable]] cardinal, [[unfoldable#Strongly unfoldable | strongly unfoldable]] cardinal
 
* [[indescribable#Totally indescribable | totally indescribable]] cardinal
 
* [[indescribable#Totally indescribable | totally indescribable]] cardinal
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* [[Transitive ZFC model]]
 
* [[Transitive ZFC model]]
 
* 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 the [[Con ZFC#Consistency hierarchy | iterated consistency $\text{Con}^\alpha(\text{ZFC})$ hierarchy]]  
+
* [[Con ZFC | Con(ZFC)]] and [[Con ZFC#Consistency hierarchy | $\text{Con}^\alpha(\text{ZFC})$]], the [[Con ZFC#Consistency hierarchy | iterated consistency hierarchy]]  
  
 
* down to [[the middle attic]]
 
* down to [[the middle attic]]

Revision as of 13:59, 3 January 2012

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.