Difference between revisions of "Upper attic"

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* '''[[huge|n-huge]]''' cardinal, [[huge | almost n-huge]] cardinal, [[huge|n-superhuge]] cardinal, [[superstrong|(n+1)-superstrong cardinal]]
 
* '''[[huge|n-huge]]''' cardinal, [[huge | almost n-huge]] cardinal, [[huge|n-superhuge]] cardinal, [[superstrong|(n+1)-superstrong cardinal]]
 
* [[high-jump]] cardinal, [[high-jump|almost high-jump]] cardinal, [[high-jump|super high-jump]] cardinal, [[high-jump|high-jump with unbounded excess closure]] cardinal
 
* [[high-jump]] cardinal, [[high-jump|almost high-jump]] cardinal, [[high-jump|super high-jump]] cardinal, [[high-jump|high-jump with unbounded excess closure]] cardinal
* [[Vopenka | Vopěnka's principle]], [[Vopenka#Vopěnka cardinals | Vopěnka]] cardinal, [[Woodin for supercompactness]] cardinal
+
* [[Vopenka | Vopěnka's principle]], [[Vopenka#Vopěnka cardinals | Vopěnka]] cardinal, [[Woodin|Woodin for supercompactness]] cardinal
 
* [[extendible]] cardinal, [[extendible | $\alpha$-extendible]] cardinal
 
* [[extendible]] cardinal, [[extendible | $\alpha$-extendible]] cardinal
* [[grand reflection]] cardinal
+
<!--* [[grand reflection]] cardinal-->
 
* [[hypercompact]] cardinal
 
* [[hypercompact]] cardinal
 
* '''[[supercompact]]''' cardinal, [[supercompact | $\lambda$-supercompact]] cardinal, [[PFA]] cardinal
 
* '''[[supercompact]]''' cardinal, [[supercompact | $\lambda$-supercompact]] cardinal, [[PFA]] cardinal
 
* '''[[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
* [[indestructible weakly compact]] cardinal
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* [[Weakly_compact#Indestructibility of a weakly compact cardinal|indestructible weakly compact]] cardinal
 
* [[subcompact]] cardinal
 
* [[subcompact]] cardinal
 
* '''[[superstrong]]''' cardinal
 
* '''[[superstrong]]''' cardinal
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* [[ineffable]] cardinal, [[weakly ineffable]] cardinal, and the $n$-ineffable cardinals hierarchy; [[completely ineffable]] cardinal
 
* [[ineffable]] cardinal, [[weakly ineffable]] cardinal, and the $n$-ineffable cardinals hierarchy; [[completely ineffable]] cardinal
 
* [[subtle]] cardinal
 
* [[subtle]] cardinal
* [[ethereal]] cardinal
+
* [[subtle#ethereal cardinals|ethereal]] cardinal
 
* [[unfoldable#superstrongly unfoldable cardinal | superstrongly unfoldable]] cardinal, [[uplifting#strongly uplifting | strongly uplifting]] cardinal  
 
* [[unfoldable#superstrongly unfoldable cardinal | superstrongly unfoldable]] cardinal, [[uplifting#strongly uplifting | strongly uplifting]] cardinal  
 
* [[uplifting#weakly superstrong cardinal | weakly superstrong]] cardinal
 
* [[uplifting#weakly superstrong cardinal | weakly superstrong]] cardinal

Revision as of 07:16, 30 October 2017

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.