Difference between revisions of "Upper attic"

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(**)
($E_i$)
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* [[Reinhardt|weakly Reinhardt]], [[Reinhardt]], [[Reinhardt|super Reinhardt]], [[Reinhardt|totally Reinhardt]] cardinal
 
* [[Reinhardt|weakly Reinhardt]], [[Reinhardt]], [[Reinhardt|super Reinhardt]], [[Reinhardt|totally Reinhardt]] cardinal
 
* the '''[[Kunen inconsistency]]'''
 
* the '''[[Kunen inconsistency]]'''
* '''[[rank into rank]]''' axioms, $C^{(n)}$-I3, $C^{(n)}$-I1, [[n-fold variants|$\omega$-fold variants]], [[L of V_lambda+1|I0 axiom]] and strengthenings
+
* '''[[rank into rank]]''' axioms ($I3$=$E_0$, $I2$=$E_1$, $E_i$, $I1$=$E_ω$ plus $m$-$C^{(n)}$-$E_i$), [[n-fold variants|$\omega$-fold variants]], [[L of V_lambda+1|I0 axiom]] and strengthenings
 
* The [[wholeness axioms]], [[I4|axioms $\mathrm{I}_4^n$]]
 
* The [[wholeness axioms]], [[I4|axioms $\mathrm{I}_4^n$]]
 
* [[n-fold variants|$n$-fold variants]] of hugeness (plus $C^{(n)}$ variants), extendibility, supercompactness, strongness, etc...
 
* [[n-fold variants|$n$-fold variants]] of hugeness (plus $C^{(n)}$ variants), extendibility, supercompactness, strongness, etc...
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<!--* [[grand reflection]] cardinal-->
 
<!--* [[grand reflection]] cardinal-->
 
* [[Supercompact#Enhanced supercompact cardinals|enhanced $\lambda$-supercompact]] cardinals, [[Supercompact#Enhanced supercompact cardinals|enhanced supercompact]] cardinal, [[hypercompact|$\lambda$-hypercompact]] cardinals, [[hypercompact]] cardinal
 
* [[Supercompact#Enhanced supercompact cardinals|enhanced $\lambda$-supercompact]] cardinals, [[Supercompact#Enhanced supercompact cardinals|enhanced supercompact]] cardinal, [[hypercompact|$\lambda$-hypercompact]] cardinals, [[hypercompact]] cardinal
* [[supercompact|$\lambda$-supercompact]] cardinals, '''[[supercompact]]''' cardinal
+
* [[supercompact|$\lambda$-supercompact]] cardinals, '''[[supercompact]]''' cardinal, [[supercompact|$C^{(n)}$-supercompact]] cardinals
 
* [[strongly compact|$\lambda$-strongly compact]] cardinals, '''[[strongly compact]]''' cardinal
 
* [[strongly compact|$\lambda$-strongly compact]] cardinals, '''[[strongly compact]]''' cardinal
 
* [[nearly supercompact]] and [[nearly supercompact#Nearly strongly compact|nearly strongly compact]] cardinals
 
* [[nearly supercompact]] and [[nearly supercompact#Nearly strongly compact|nearly strongly compact]] cardinals

Revision as of 12:10, 23 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.