A SIMPLIFIED ORDINAL ANALYSIS OF FIRST-ORDER REFLECTION
Toshiyasu Arai · Journal of Symbolic Logic · 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.