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Andreas Weiermann (1990)
Ein neuer Zugang zu Kollabierungsfunktionen
J. Barwise (1975)
Admissible sets and structures
M. Rathjen (1994)
Collapsing functions based on recursively large ordinals: A well-ordering proof for KPMArchive for Mathematical Logic, 33
G. Jäger (1980)
Zur Beweistheorie Der Kripke-Platek-Mengenlehre Über Den Natürlichen ZahlenArchiv für mathematische Logik und Grundlagenforschung, 22
M. Rathjen (1991)
Proof-theoretic analysis of KPMArchive for Mathematical Logic, 30
Wilfried Buchholz (1975)
Normalfunktionen und Konstruktive Systeme von Ordinalzahlen
Wayne Richter, P. Aczel (1974)
Inductive Definitions and Reflecting Properties of Admissible OrdinalsStudies in logic and the foundations of mathematics, 79
In this paper we introduce a recursive notation system $O(\mu)$ of ordinals. An element of the notation system is called an ordinal diagram following G. Takeuti [25]. The system is designed for proof theoretic study of theories of recursively Mahlo universes. We show that for each $\alpha<\Omega$ in $O(\mu)$ KPM proves that the initial segment of $O(\mu)$ determined by $\alpha$ is a well ordering. Proof theoretic study for such theories will be reported in [9].
Archive for Mathematical Logic – Springer Journals
Published: Jul 1, 2000
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