A Simplified Ordinal Analysis of First-Order Reflection

Journal of Symbolic Logic 85 (3):1163-1185 (2020)
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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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10.1017/jsl.2020.23

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Citations of this work

Wellfoundedness proof with the maximal distinguished set.Toshiyasu Arai - 2023 - Archive for Mathematical Logic 62 (3):333-357.

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References found in this work

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.
Provably Recursive Functions of Reflection.Wolfram Pohlers & Jan–Carl Stegert - 2012 - In Ulrich Berger, Hannes Diener, Peter Schuster & Monika Seisenberger (eds.), Logic, Construction, Computation. De Gruyter. pp. 381-474.

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