Proof-theoretic dilator and intermediate pointclasses
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910237402857472 |
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| author | Jeon, Hanul |
| author_facet | Jeon, Hanul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proof-theoretic dilator and intermediate pointclasses Jeon, Hanul Logic 03F07, 03F15, 03D60, 03F35 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. |
| title | Proof-theoretic dilator and intermediate pointclasses |
| topic | Logic 03F07, 03F15, 03D60, 03F35 |
| url | https://arxiv.org/abs/2501.11220 |