Difference between revisions of "Upper attic"

From Cantor's Attic
Jump to: navigation, search
 
Line 39: Line 39:
 
* [[Ramsey#Strongly Ramsey cardinal|strongly Ramsey]] cardinal, [[Ramsey|strongly Ramsey M-rank]], [[Ramsey#Super Ramsey cardinal|super Ramsey]] cardinal, [[Ramsey|super Ramsey M-rank]]
 
* [[Ramsey#Strongly Ramsey cardinal|strongly Ramsey]] cardinal, [[Ramsey|strongly Ramsey M-rank]], [[Ramsey#Super Ramsey cardinal|super Ramsey]] cardinal, [[Ramsey|super Ramsey M-rank]]
 
* $\alpha$-[[filter property]], [[Ramsey|$\alpha$-Ramsey]] cardinal &#40;for $\omega < \alpha < \kappa$), [[Ramsey|almost fully Ramsey]] &#40;=[[Ramsey|$<κ$-Ramsey]]) cardinal  
 
* $\alpha$-[[filter property]], [[Ramsey|$\alpha$-Ramsey]] cardinal &#40;for $\omega < \alpha < \kappa$), [[Ramsey|almost fully Ramsey]] &#40;=[[Ramsey|$<κ$-Ramsey]]) cardinal  
* [[Ramsey|$\Pi_\alpha$-Ramsey]], [[Ramsey|completely Romsey]] &#40;=[[Ramsey|$ω$-very Ramsey]]), [[Ramsey|$\alpha$-hyper completely Romsey]], [[Ramsey|super completely Romsey]] cardinals
+
* [[Ramsey|$\Pi_\alpha$-Ramsey]], [[Ramsey|completely Ramsey]] &#40;=[[Ramsey|$ω$-very Ramsey]]), [[Ramsey|$\alpha$-hyper completely Ramsey]], [[Ramsey|super completely Ramsey]] cardinals
 
* [[Ramsey|$\alpha$-Mahlo–Ramsey]] hierarchy
 
* [[Ramsey|$\alpha$-Mahlo–Ramsey]] hierarchy
 
* [[Ramsey|Ramsey M-rank]]
 
* [[Ramsey|Ramsey M-rank]]

Latest revision as of 19:22, 29 July 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.