Difference between revisions of "Middle attic"

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* Up to the [[upper attic]]
 
* Up to the [[upper attic]]
 
* fully [[reflecting]] cardinals $V_\delta\prec V$ and the [[reflecting#Feferman theory | Feferman theory]]
 
* fully [[reflecting]] cardinals $V_\delta\prec V$ and the [[reflecting#Feferman theory | Feferman theory]]
* [[reflecting | $\Sigma_n$-reflecting]] cardinals
+
* [[reflecting#Sigma2 reflecting | $\Sigma_2$ reflecting]] and [[reflecting | $\Sigma_n$-reflecting]] cardinals
* [[reflecting#Sigma2 reflecting | $\Sigma_2$ reflecting cardinal]]
+
 
* [[beth#beth_fixed_point | $\beth$-fixed point]]
 
* [[beth#beth_fixed_point | $\beth$-fixed point]]
 
* the [[beth | $\beth_\alpha$ hierarchy]]
 
* the [[beth | $\beth_\alpha$ hierarchy]]

Revision as of 17:33, 29 December 2011

St. Augustine Lighthouse photo by Madrigar

Welcome to the middle attic, where the uncountable cardinals, that solid stock of mathematics, begin their endless upward structural progession. Here, we survey the infinite cardinals whose existence can be proved in, or is at least equiconsistent with, the ZFC axioms of set theory.