Difference between revisions of "Middle attic"

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* [[beth omega | $\beth_\omega$]] and the [[strong limit]] cardinals
 
* [[beth omega | $\beth_\omega$]] and the [[strong limit]] cardinals
 
* the [[continuum]]
 
* the [[continuum]]
* [[cardinal characteristics of the continuum]]
+
* [[cardinal characteristics]]  of the continuum
 
** 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
 
* [[aleph#aleph fixed point | $\aleph$-fixed point]]
 
* [[aleph#aleph fixed point | $\aleph$-fixed point]]

Revision as of 06:31, 9 January 2012

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.