Difference between revisions of "Upper attic"

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(some new)
(, completely remarkable)
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* the [[Ramsey#.24.5Calpha.24-iterable cardinal|$n$-iterable]] and [[huge|virtually $n$-huge*]] hierarchy
 
* the [[Ramsey#.24.5Calpha.24-iterable cardinal|$n$-iterable]] and [[huge|virtually $n$-huge*]] hierarchy
 
* [[Woodin|virtually Shelah for supercompactness]] cardinal
 
* [[Woodin|virtually Shelah for supercompactness]] cardinal
* [[extendible|virtually extendible]], [[extendible|virtually $C^{(n)}$-extendible]] cardinal
+
* [[extendible|virtually extendible]] (=[[remarkable|$2$-remarkable]]), [[extendible|virtually $C^{(n)}$-extendible]] (=[[remarkable|$n+1$-remarkable]]) cardinals, [[remarkable|completely remarkable]] cardinal, [[Vopenka|Generic Vopěnka's Principle]]
* [[remarkable|$n$-remarkable]], [[Vopenka|Generic Vopěnka's Principle]]
+
 
* [[remarkable|($1$-)remarkable]] (=virtually supercompact), [[measurable|virtually measurable]], [[Ramsey|strategic $\omega$-Ramsey]] cardinals, [[proper forcing axiom|weak Proper Forcing Axiom]]
 
* [[remarkable|($1$-)remarkable]] (=virtually supercompact), [[measurable|virtually measurable]], [[Ramsey|strategic $\omega$-Ramsey]] cardinals, [[proper forcing axiom|weak Proper Forcing Axiom]]
 
* [[Ramsey#.24.5Calpha.24-iterable cardinal|weakly Ramsey]] (=$1$-iterable) cardinal, [[Ramsey|super weakly Ramsey]] cardinals, [[Ramsey|$\omega$-Ramsey]] cardinal
 
* [[Ramsey#.24.5Calpha.24-iterable cardinal|weakly Ramsey]] (=$1$-iterable) cardinal, [[Ramsey|super weakly Ramsey]] cardinals, [[Ramsey|$\omega$-Ramsey]] cardinal

Revision as of 13:11, 11 September 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.