Ordinal collapsing function: Difference between revisions

Revision as of 18:21, 10 May 2008

Revision as of 21:09, 4 November 2008

Line 198:

* The same author<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.

* Even more recently, the same author 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).

== Notes ==

<references/>

== References ==

Line 209 ⟶ 212:

* {{cite journal | last=Rathjen | first=Michael | title=An ordinal analysis of stability | journal=Archive for Mathematical Logic | volume=44 | year=2005 | pages=1&ndash;62 | url=http://www.maths.leeds.ac.uk/~rathjen/NSTAB.ps }}

* {{cite web | url=http://www.mathematik.uni-muenchen.de/~aehlig/EST/rathjen4.pdf | title=Proof Theory: Part III, Kripke-Platek Set Theory | accessdate=2008-04-17 | last=Rathjen | first=Michael | date=August 2005 }} (slides of a talk given at Fischbachau)

== Notes ==

<references/>

[[Category:Ordinal numbers]]