Proof-theoretic dilator and intermediate pointclasses
Logic
2026-05-21 v2
Abstract
There are two major generalizations of the standard ordinal analysis: One is Girard's -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 are assigned to theories. In this paper, we show that these two are systematically entangled, and -proof theoretic analysis has a critical role in connecting these two.
Cite
@article{arxiv.2501.11220,
title = {Proof-theoretic dilator and intermediate pointclasses},
author = {Hanul Jeon},
journal= {arXiv preprint arXiv:2501.11220},
year = {2026}
}
Comments
44 pages. The proof of Theorem 5.19 was incorrect, so replaced by a new proof. The $\beta$-proof system now follows Tait-styled calculus instead of two-sided sequent calculus. Added explanations for Pohlers' framework in the introduction