A simplified ordinal analysis of first-order reflection

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.

arXiv admin note: substantial text overlap with arXiv:1506.05280

References in corpus (1)

• Iterating the recursively Mahlo operations