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Ordinal diagrams for recursively Mahlo universes

Ordinal diagrams for recursively Mahlo universes 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]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Ordinal diagrams for recursively Mahlo universes

Archive for Mathematical Logic , Volume 39 (5) – Jul 1, 2000

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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s001530050153
Publisher site
See Article on Publisher Site

Abstract

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].

Journal

Archive for Mathematical LogicSpringer Journals

Published: Jul 1, 2000

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