Ordinal collapsing function: Difference between revisions

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== References ==
* {{cite journal | last=Takeuti | first=Gaisi | authorlink=Gaisi Takeuti | title=Consistency proofs of subsystems of classical analysis | journal=Annals of Mathematics | volume=86 | year=1967 | pages=299–348 | doi=10.2307/1970691 }}
* {{cite journal | last=Jäger | first=Gerhard | coauthors=Pohlers, Wolfram | title=Eine beweistheoretische Untersuchung von (<math>\Delta^1_2</math>-CA)+(BI) und verwandter Systeme | journal=Bayerische Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Klasse Sitzungsberichte | volume=1982 | year=1983 | pages=1&ndash;28 }}
* {{cite journal | last=Buchholz | first=Wilfried | title=A New System of Proof-Theoretic Ordinal Notations | journal=Annals of Pure and Applied Logic | volume=32 | year=1986 | pages=195&ndash;207 | doi=10.1016/0168-0072(86)90052-7 }}
* {{cite journal | last=Rathjen | first=Michael | title=Proof-theoretic analysis of KPM | journal=Archive for Mathematical Logic | volume=30 | year=1991 | pages=377&ndash;403 | doi=10.1007/BF01621475 }}
* {{cite journal | last=Rathjen | first=Michael | title=Proof theory of reflection | journal=Annals of Pure and Applied Logic | volume=68 | year=1994 | pages=181&ndash;224 | url=http://www.maths.leeds.ac.uk/~rathjen/ehab.pdf | doi=10.1016/0168-0072(94)90074-4 }}
* {{cite journal | last=Rathjen | first=Michael | title=Recent Advances in Ordinal Analysis: <math>\Pi^1_2</math>-CA and Related Systems | journal=The Bulletin of Symbolic Logic | volume=1 | year=1995 | pages=468&ndash;485 | url=http://www.maths.leeds.ac.uk/~rathjen/bulf.ps | doi=10.2307/421132 | format={{dead link|date=April 2009}} &ndash; <sup>[http://scholar.google.co.uk/scholar?hl=en&lr=&q=author%3ARathjen+intitle%3ARecent+Advances+in+Ordinal+Analysis%3A+%3Cmath%3E%5CPi%5E1_2%3C%2Fmath%3E-CA+and+Related+Systems&as_publication=The+Bulletin+of+Symbolic+Logic&as_ylo=1995&as_yhi=1995&btnG=Search Scholar search]</sup> }}
* {{cite journal | last=Kahle | first=Reinhard | title=Mathematical proof theory in the light of ordinal analysis | journal=Synthese | volume=133 | year=2002 | pages=237&ndash;255 | doi=10.1023/A:1020892011851 }}
* {{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 | doi=10.1007/s00153-004-0226-2 }}
* {{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)