Difference between revisions of "Upper attic"

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(BTEE)
(BTEE < completely ineffable)
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* the [[Erdos|$\alpha$-'''Erdős''']], [[Ramsey#.24.5Calpha.24-iterable cardinal|$\alpha$-iterable]] and [[Ramsey|$(\omega, \alpha)$-Ramsey]] hierarchy for countable infinite $\alpha$
 
* the [[Erdos|$\alpha$-'''Erdős''']], [[Ramsey#.24.5Calpha.24-iterable cardinal|$\alpha$-iterable]] and [[Ramsey|$(\omega, \alpha)$-Ramsey]] hierarchy for countable infinite $\alpha$
 
* [[Erdos|$\omega$-Erdős]] cardinal, [[remarkable|weakly remarkable]] cardinal that is not remarkable
 
* [[Erdos|$\omega$-Erdős]] cardinal, [[remarkable|weakly remarkable]] cardinal that is not remarkable
* [[Basic Theory of Elementary Embeddings]] ([[BTEE|$\mathrm{BTEE}$]])
 
 
* [[rank into rank|virtually rank-into-rank]] cardinal
 
* [[rank into rank|virtually rank-into-rank]] cardinal
 
* 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
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* [[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
 
* [[completely ineffable]] cardinal (= $\omega$-[[filter property]])
 
* [[completely ineffable]] cardinal (= $\omega$-[[filter property]])
 +
* [[Basic Theory of Elementary Embeddings]] ([[BTEE|$\mathrm{BTEE}$]])
 
* [[ineffable#Helix|the $n$-subtle, $n$-almost ineffable, $n$-ineffable cardinals' hierarchy]]
 
* [[ineffable#Helix|the $n$-subtle, $n$-almost ineffable, $n$-ineffable cardinals' hierarchy]]
 
* [[Ramsey|$n$-Ramsey]], [[Ramsey|genuine $n$-Ramsey]], [[Ramsey|normal $n$-Ramsey]], [[Ramsey|$<\omega$-Ramsey]] cardinals
 
* [[Ramsey|$n$-Ramsey]], [[Ramsey|genuine $n$-Ramsey]], [[Ramsey|normal $n$-Ramsey]], [[Ramsey|$<\omega$-Ramsey]] cardinals

Revision as of 13:18, 8 November 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.