Difference between revisions of "Upper attic"

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* [[ORD is Mahlo|$\text{Ord}$ is Mahlo]]
 
* [[ORD is Mahlo|$\text{Ord}$ is Mahlo]]
 
* [[reflecting#Sigma_2 correct cardinals | $\Sigma_2$-reflecting]], [[reflecting | $\Sigma_n$-reflecting]] and [[reflecting]] cardinals
 
* [[reflecting#Sigma_2 correct cardinals | $\Sigma_2$-reflecting]], [[reflecting | $\Sigma_n$-reflecting]] and [[reflecting]] cardinals
 +
* [[Jäger's collapsing functions and ρ-inaccessible ordinals]]
 
* [[inaccessible#Degrees of inaccessibility | $1$-inaccessible]], the [[inaccessible#Degrees of inaccessibility | $\alpha$-inaccessible]] hierarchy and  [[inaccessible#Hyper-inaccessible | hyper-inaccessible]] cardinals
 
* [[inaccessible#Degrees of inaccessibility | $1$-inaccessible]], the [[inaccessible#Degrees of inaccessibility | $\alpha$-inaccessible]] hierarchy and  [[inaccessible#Hyper-inaccessible | hyper-inaccessible]] cardinals
 
* [[inaccessible#Universes | Grothendieck universe axiom]], equivalent to the existence of a proper class of [[inaccessible]] cardinals
 
* [[inaccessible#Universes | Grothendieck universe axiom]], equivalent to the existence of a proper class of [[inaccessible]] cardinals

Revision as of 07:31, 19 May 2018

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.