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arXiv · 1907.07611

A simplified ordinal analysis of first-order reflection

Toshiyasu Arai
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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.

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Toshiyasu Arai. 2019-07-12. A simplified ordinal analysis of first-order reflection. https://doi.org/10.1017/jsl.2020.23

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