Difference between revisions of "Middle attic"

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(reflecting cardinals)
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* into the [[upper attic]]
 
* into the [[upper attic]]
* [[correct]] cardinals, [[reflecting | $V_\delta\prec V$]] and the [[reflecting#Feferman theory | Feferman theory]]
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* [[correct]] cardinals, [[reflecting cardinals| $V_\delta\prec V$]] and the [[reflecting cardinals#Feferman theory|Feferman theory]]
* [[reflecting#Sigma_2 correct cardinals | $\Sigma_2$ correct]] and [[reflecting | $\Sigma_n$-correct]] cardinals
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* [[Reflecting_cardinals#.24.5CSigma_2.24-correct_cardinals|$\Sigma_2$ correct]] and [[correct|$\Sigma_n$-correct]] cardinals
 
* [[extendible#-extendible cardinals | 0-extendible]] cardinal
 
* [[extendible#-extendible cardinals | 0-extendible]] cardinal
 
* [[extendible#Sigma_n-extendible cardinals|$\Sigma_n$-extendible]] cardinal
 
* [[extendible#Sigma_n-extendible cardinals|$\Sigma_n$-extendible]] cardinal

Revision as of 22:39, 2 August 2021

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.