Journal of Symbolic Logic 85 (3):1163-1185 (2020)

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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DOI 10.1017/jsl.2020.23
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References found in this work BETA

Proof Theory of Reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
An Ordinal Analysis of Stability.Michael Rathjen - 2005 - Archive for Mathematical Logic 44 (1):1-62.
Ordinal Diagrams for Recursively Mahlo Universes.Toshiyasu Arai - 2000 - Archive for Mathematical Logic 39 (5):353-391.

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