Difference between revisions of "Upper attic"

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m (consistency strength of strongly tall cardinals is known)
m
 
Line 27: Line 27:
 
* The '''[[axiom of determinacy]]''' and [[axiom of projective determinacy|its projective counterpart]]
 
* The '''[[axiom of determinacy]]''' and [[axiom of projective determinacy|its projective counterpart]]
 
* '''[[Woodin]]''' cardinal
 
* '''[[Woodin]]''' cardinal
* [[tall|strongly tall]] cardinals
+
* [[strongly tall]] cardinal
 
* [[strong]] cardinal and the [[strong | $\theta$-strong]] and [[strong#Hypermeasurable | hypermeasurability]] hierarchies, [[tall]] cardinal, [[tall|$\theta$-tall]] hierarchy
 
* [[strong]] cardinal and the [[strong | $\theta$-strong]] and [[strong#Hypermeasurable | hypermeasurability]] hierarchies, [[tall]] cardinal, [[tall|$\theta$-tall]] hierarchy
 
* Nontrivial [[Mitchell rank]], [[Mitchell rank | $o(\kappa)=1$]], [[Mitchell rank | $o(\kappa)=\kappa^{++}$]]  
 
* Nontrivial [[Mitchell rank]], [[Mitchell rank | $o(\kappa)=1$]], [[Mitchell rank | $o(\kappa)=\kappa^{++}$]]  

Latest revision as of 09:55, 10 October 2018

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.