Difference between revisions of "Upper attic"

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* [[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 | $o(\kappa)=\kappa^{++}$]]  
* [[zero dagger| $0^\dagger$]]
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* '''[[measurable]]''' cardinal, [[zero dagger| $0^\dagger$]] (''zero-dagger''), [[weakly measurable]] cardinal, singular [[Jonsson|Jónsson]] cardinal
* '''[[measurable]]''' cardinal, [[weakly measurable]] cardinal, singular [[Jonsson|Jónsson]] cardinal
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* '''[[Ramsey]]''' cardinal, [[Jonsson | Jónsson]] cardinal, [[Rowbottom]] cardinal, [[strongly Ramsey]] cardinal, [[virtually Ramsey]] cardinal
 
* '''[[Ramsey]]''' cardinal, [[Jonsson | Jónsson]] cardinal, [[Rowbottom]] cardinal, [[strongly Ramsey]] cardinal, [[virtually Ramsey]] cardinal
 
* [[Erdos | $\omega_1$-Erdős]] cardinal and [[Erdos | $\gamma$-Erdős]] cardinals for uncountable $\gamma$  
 
* [[Erdos | $\omega_1$-Erdős]] cardinal and [[Erdos | $\gamma$-Erdős]] cardinals for uncountable $\gamma$  

Revision as of 11:39, 14 December 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.