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A SIMPLIFIED ORDINAL ANALYSIS OF FIRST-ORDER REFLECTION

Part of: Proof theory and constructive mathematics

Published online by Cambridge University Press:  23 October 2020

TOSHIYASU ARAI
TOSHIYASU ARAI*
Affiliation:
GRADUATE SCHOOL OF SCIENCE, CHIBA UNIVERSITY 1-33, YAYOI-CHO, INAGE-KU, CHIBA, 263-8522, JAPAN Current address: GRADUATE SCHOOL OF MATHEMATICAL SCIENCES, UNIVERSITY OF TOKYO 3-8-1 KOMABA, MEGURO-KU, TOKYO153-8914, JAPANE-mail: [email protected]
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Abstract

In this note we give a simplified ordinal analysis of first-order reflection. An ordinal notation system $OT$ is introduced based on $\psi $ -functions. Provable $\Sigma _{1}$ -sentences on $L_{\omega _{1}^{CK}}$ are bounded through cut-elimination on operator controlled derivations.

Keywords

ordinalsMahlo classes

MSC classification

Primary: 03F99: None of the above, but in this section
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 3 , September 2020 , pp. 1163 - 1185
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Copyright
© The Association for Symbolic Logic 2020

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References

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