English

A simplified ordinal analysis of first-order reflection

Logic 2021-07-01 v1

Abstract

In this note we give a simplified ordinal analysis of first-order reflection. An ordinal notation system OTOT is introduced based on ψ\psi-functions. Provable Σ1\Sigma_{1}-sentences on Lω1CKL_{\omega_{1}^{CK}} are bounded through cut-elimination on operator controlled derivations.

Cite

@article{arxiv.1907.07611,
  title  = {A simplified ordinal analysis of first-order reflection},
  author = {Toshiyasu Arai},
  journal= {arXiv preprint arXiv:1907.07611},
  year   = {2021}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1506.05280

R2 v1 2026-06-23T10:23:23.842Z