Difference between revisions of "Middle attic"

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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]]
 
* [[correct]] cardinals, [[reflecting | $V_\delta\prec V$]] and the [[reflecting#Feferman theory | Feferman theory]]
* [[reflecting#$\Sigma_2$ correct cardinals | $\Sigma_2$ correct]] and [[reflecting | $\Sigma_n$-correct]] cardinals
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* [[reflecting#Sigma_2 correct cardinals | $\Sigma_2$ correct]] and [[reflecting | $\Sigma_n$-correct]] cardinals
* [[0-extendible]] cardinal
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* [[extendible#-extendible cardinals | 0-extendible]] cardinal
* [[extendible#$\Sigma_n$-extendible cardinals | $\Sigma_n$-extendible ]] cardinal
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* [[extendible#Sigma_n-extendible cardinals|$\Sigma_n$-extendible]] cardinal
 
* [[beth#beth_fixed_point | $\beth$-fixed point]]
 
* [[beth#beth_fixed_point | $\beth$-fixed point]]
 
* the [[beth]] numbers and the [[beth | $\beth_\alpha$ hierarchy]]
 
* the [[beth]] numbers and the [[beth | $\beth_\alpha$ hierarchy]]
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* [[aleph#aleph fixed point | $\aleph$-fixed point]]
 
* [[aleph#aleph fixed point | $\aleph$-fixed point]]
 
* the [[aleph]] numbers and the [[aleph | $\aleph_\alpha$ hierarchy]]
 
* the [[aleph]] numbers and the [[aleph | $\aleph_\alpha$ hierarchy]]
 +
* [[Buchholz's ψ functions]]
 
* [[aleph#aleph omega | $\aleph_\omega$]] and [[singular]] cardinals
 
* [[aleph#aleph omega | $\aleph_\omega$]] and [[singular]] cardinals
 
* [[aleph#aleph two | $\aleph_2$]], the second uncountable cardinal
 
* [[aleph#aleph two | $\aleph_2$]], the second uncountable cardinal

Latest revision as of 06:24, 19 May 2018

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.