Content deleted Content added
m →Collapsing large cardinals: Copyedit (major) |
Baking Soda (talk | contribs) create section →See also: ; add * Forcing (mathematics) |
||
Line 216:
* Rathjen<ref>Rathjen, 1994 (Ann. Pure Appl. Logic)</ref> later described the collapse of a [[weakly compact cardinal]] to describe the ordinal-theoretic strength of Kripke-Platek set theory augmented by certain [[reflection principle]]s (concentrating on the case of <math>\Pi_3</math>-reflection). Very roughly speaking, this proceeds by introducing the first cardinal <math>\Xi(\alpha)</math> which is <math>\alpha</math>-hyper-Mahlo and adding the <math>\alpha \mapsto \Xi(\alpha)</math> function itself to the collapsing system.
* Rathjen has begun<ref>Rathjen, 2005 (Arch. Math. Logic)</ref> the investigation of the collapse of yet larger cardinals, with the ultimate goal of achieving an ordinal analysis of <math>\Pi^1_2</math>-comprehension (which is proof-theoretically equivalent to the augmentation of Kripke-Platek by <math>\Sigma_1</math>-separation).
== See also ==
* [[Forcing (mathematics)]]
== Notes ==
| |||