Difference between revisions of "Upper attic"

From Cantor's Attic
Jump to: navigation, search
(C(n))
(Misrepresents the other of large cardinals. Hyperhuge=2-Supercompact>2-Strong)
 
Line 11: Line 11:
 
* The [[wholeness axioms]], [[I4|axioms $\mathrm{I}_4^n$]]
 
* The [[wholeness axioms]], [[I4|axioms $\mathrm{I}_4^n$]]
 
* [[n-fold variants]] of hugeness (plus $C^{(n)}$ variants), extendibility, supercompactness, strongness, etc...
 
* [[n-fold variants]] of hugeness (plus $C^{(n)}$ variants), extendibility, supercompactness, strongness, etc...
* [[huge|almost huge]], '''[[huge]]''', [[huge|huge*]], [[huge|super almost huge]], [[huge|superhuge]], [[huge|hyperhuge]], [[huge|ultrahuge]], [[superstrong|2-superstrong]] cardinal
+
* [[huge|almost huge]], '''[[huge]]''', [[huge|huge*]], [[huge|super almost huge]], [[huge|superhuge]], [[huge|ultrahuge]], [[superstrong|2-superstrong]] cardinal
 
* [[high-jump]] cardinal, [[high-jump|almost high-jump]] cardinal, [[high-jump|super high-jump]] cardinal, [[high-jump|high-jump with unbounded excess closure]] cardinal
 
* [[high-jump]] cardinal, [[high-jump|almost high-jump]] cardinal, [[high-jump|super high-jump]] cardinal, [[high-jump|high-jump with unbounded excess closure]] cardinal
 
* [[Woodin#Shelah cardinals|Shelah for supercompactness]]
 
* [[Woodin#Shelah cardinals|Shelah for supercompactness]]

Latest revision as of 20:41, 8 October 2019

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.