Cut-elimination for $\omega_{1}$

TL;DR

This paper analyzes the proof-theoretic strength of a specific Kripke-Platek set theory with certain axioms, using ordinal-based calibration under the assumption of an uncountable regular ordinal.

Contribution

It provides a new calibration of the strength of Kripke-Platek set theory with Infinity and -Collection axioms assuming an uncountable regular ordinal.

Findings

Calibrates the soundness strength of the set theory using ordinal analysis.

Establishes a connection between set-theoretic axioms and ordinal existence.

Advances understanding of proof-theoretic strength in set theory.

Abstract

In this paper we calibrate the strength of the soundness of a Kripke-Platek set theory with the axioms of Infinity and \Pi_{1}-Collection with the assumption that`there exists an uncountable regular ordinal' in terms of the existence of ordinals.