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arXiv · 2501.11220

Proof-theoretic dilator and intermediate pointclasses

Hanul Jeon
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Abstract

There are two major generalizations of the standard ordinal analysis: One is Girard's $Π^1_2$-proof theory in which dilators are assigned to theories instead of ordinals. The other is Pohlers' generalized ordinal analysis with Spector classes, where ordinals greater than $ω_1^{\mathsf{CK}}$ are assigned to theories. In this paper, we show that these two are systematically entangled, and $Σ^1_2$-proof theoretic analysis has a critical role in connecting these two.

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Hanul Jeon. 2026-05-19. Proof-theoretic dilator and intermediate pointclasses. https://arxiv.org/abs/2501.11220

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