Difference between revisions of "Middle attic"

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** the [[bounding number | bounding number $\frak{b}$]], the [[dominating number | dominating number $\frak{d}$]], the [[covering number | covering numbers]], [[additivity number | additivity numbers]] and many more
 
** the [[bounding number | bounding number $\frak{b}$]], the [[dominating number | dominating number $\frak{d}$]], the [[covering number | covering numbers]], [[additivity number | additivity numbers]] and many more
 
* the [[descriptive set theory | descriptive set-theoretic]] cardinals
 
* the [[descriptive set theory | descriptive set-theoretic]] cardinals
 +
* [[Karauwan cardinal| Karauwan]] cardinals, and Rayo length catching points
 
* [[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]]

Revision as of 04:49, 26 July 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.