Difference between revisions of "Upper attic"

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Welcome to the upper attic, the transfinite realm of large cardinals, the higher infinite, carrying us upward from the merely inaccessible and indescribable to the subtle and endlessly extendible concepts beyond, towards the calamity of inconsistency.  
 
Welcome to the upper attic, the transfinite realm of large cardinals, the higher infinite, carrying us upward from the merely inaccessible and indescribable to the subtle and endlessly extendible concepts beyond, towards the calamity of inconsistency.  
  
* [[hypercompact|excessively hypercompact cardinal]] (inconsistent with the axiom of choice)
+
* [[hypercompact|excessively hypercompact cardinal]] (inconsistent)
 
* The [[Kunen inconsistency]]: [[Reinhardt]] cardinal, [[Kunen_inconsistency#Super_Reinhardt_cardinal | super Reinhardt]] cardinal, [[Berkeley]] cardinal
 
* The [[Kunen inconsistency]]: [[Reinhardt]] cardinal, [[Kunen_inconsistency#Super_Reinhardt_cardinal | super Reinhardt]] cardinal, [[Berkeley]] cardinal
 
* [[Rank into rank]] cardinals $j:V_\lambda\to V_\lambda$, [[rank+1 into rank+1]] cardinal $j:V_{\lambda+1}\to V_{\lambda+1}$, I0 cardinal [[L of V_lambda+1 | $j:L(V_{\lambda+1})\to L(V_{\lambda+1})$]]
 
* [[Rank into rank]] cardinals $j:V_\lambda\to V_\lambda$, [[rank+1 into rank+1]] cardinal $j:V_{\lambda+1}\to V_{\lambda+1}$, I0 cardinal [[L of V_lambda+1 | $j:L(V_{\lambda+1})\to L(V_{\lambda+1})$]]

Revision as of 11:55, 11 September 2017

Cape Pogue Lighthouse photo by Timothy Valentine

Welcome to the upper attic, the transfinite realm of large cardinals, the higher infinite, carrying us upward from the merely inaccessible and indescribable to the subtle and endlessly extendible concepts beyond, towards the calamity of inconsistency.