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1 results

A SIMPLIFIED ORDINAL ANALYSIS OF FIRST-ORDER REFLECTION
Part of
- Proof theory and constructive mathematics
TOSHIYASU ARAI
Journal:

The Journal of Symbolic Logic / Volume 85 / Issue 3 / September 2020

Published online by Cambridge University Press:

23 October 2020, pp. 1163-1185

Print publication:

September 2020
- Article
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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.