Dilator-based analysis of KP

Hanul Jeon

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arXiv · 2608.29157

Dilator-based analysis of KP

Hanul Jeon

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Abstract

Proof theorists developed various frameworks to analyze impredicative systems like $\Pi^1_1\text{-}\mathsf{CA}_0$ or $\mathsf{KP}$; One is an operator-controlled derivation system, and the other is Girard's dilator-based $\beta$-logic. In this paper, we provide a functorial formulation of operator-controlled analysis of $\mathsf{KP}$, thereby unifying the two approaches into a single framework. As an application, a new proof of Girard's boundedness theorem is also provided, which states that every $\Sigma_1$-over-$L_{\omega_1^{\mathsf{CK}}}$-definable function $\omega_1^\mathsf{CK}\to \omega_1^\mathsf{CK}$ is bounded by a recursive dilator.

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BibTeX RIS

Hanul Jeon. 2026-08-29. Dilator-based analysis of KP. https://arxiv.org/abs/2608.29157

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