Difference between revisions of "Middle attic"

From Cantor's Attic
Jump to: navigation, search
Line 17: Line 17:
 
* [[uncountable]], [[regular]] and [[aleph#successor cardinals | successor]] cardinals
 
* [[uncountable]], [[regular]] and [[aleph#successor cardinals | successor]] cardinals
 
* [[aleph#aleph one | $\aleph_1$]], the first [[uncountable]] cardinal
 
* [[aleph#aleph one | $\aleph_1$]], the first [[uncountable]] cardinal
* [[cardinal | cardinals]], [[cardinal#infinite | infinite]] cardinals
+
* [[cardinal | cardinals]], [[infinite]] cardinals
 
* [[Aleph zero | $\aleph_0$]] and the rest of the [[lower attic]]
 
* [[Aleph zero | $\aleph_0$]] and the rest of the [[lower attic]]

Revision as of 04:24, 3 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.