Difference between revisions of "Upper attic"

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(this guesses seem to be closer)
(links)
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* [[uplifting#pseudo uplifting cardinal|pseudo uplifting]] cardinal, [[uplifting]] cardinal
 
* [[uplifting#pseudo uplifting cardinal|pseudo uplifting]] cardinal, [[uplifting]] cardinal
 
* [[ORD is Mahlo|$\text{Ord}$ is Mahlo]]<!-- apparently equiconsistent with a reflecting cardinal -->
 
* [[ORD is Mahlo|$\text{Ord}$ is Mahlo]]<!-- apparently equiconsistent with a reflecting cardinal -->
* [[reflecting#Sigma_2 correct cardinals|$\Sigma_2$-reflecting]], [[reflecting|$\Sigma_n$-reflecting]] and [[reflecting]] cardinals
+
* [[reflecting cardinals#.24.5CSigma_2.24-correct_cardinals|$\Sigma_2$-reflecting]], [[reflecting cardinals|$\Sigma_n$-reflecting]] and [[reflecting cardinals]]
 
* [[Mahlo|$\Sigma_n$-Mahlo]], [[weakly compact|$\Sigma_n$-weakly compact]], [[Mahlo|$\Sigma_\omega$-Mahlo]] and [[weakly compact|$\Sigma_\omega$-weakly compact]]<!-- Really? In particular, are $\Sigma_\omega$ variants not stronger then ORD is Mahlo? Maybe $\Sigma_\omega$-weakly compact is even stronger than Mahlo? --> cardinals
 
* [[Mahlo|$\Sigma_n$-Mahlo]], [[weakly compact|$\Sigma_n$-weakly compact]], [[Mahlo|$\Sigma_\omega$-Mahlo]] and [[weakly compact|$\Sigma_\omega$-weakly compact]]<!-- Really? In particular, are $\Sigma_\omega$ variants not stronger then ORD is Mahlo? Maybe $\Sigma_\omega$-weakly compact is even stronger than Mahlo? --> cardinals
 
* [[Jäger's collapsing functions and ρ-inaccessible ordinals]]  
 
* [[Jäger's collapsing functions and ρ-inaccessible ordinals]]  

Revision as of 12:42, 14 May 2022

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.