Generalizing Goodstein's theorem and Cichon's independence proof
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918481966923776 |
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| author | Wilken, Gunnar |
| author_facet | Wilken, Gunnar |
| contents | We generalize Goodstein's theorem (Goodstein 1944) and Cichon's independence proof (Cichon 1983) to $Π^1_1-\mathrm{CA}_0$ using results from (Wilken 2026). The method is generalizable to stronger notation systems that provide unique terms for ordinals and enjoy Bachmann property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalizing Goodstein's theorem and Cichon's independence proof Wilken, Gunnar Logic 03F40, 03D20, 03D60, 03F15 We generalize Goodstein's theorem (Goodstein 1944) and Cichon's independence proof (Cichon 1983) to $Π^1_1-\mathrm{CA}_0$ using results from (Wilken 2026). The method is generalizable to stronger notation systems that provide unique terms for ordinals and enjoy Bachmann property. |
| title | Generalizing Goodstein's theorem and Cichon's independence proof |
| topic | Logic 03F40, 03D20, 03D60, 03F15 |
| url | https://arxiv.org/abs/2511.04526 |