Generalizing Goodstein's theorem and Cichon's independence proof

2025/11/06 by Gunnar Wilken, Wilken, Gunnar
Mathematics · #03D20 #03D60 #03F15 #03F40 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2511.04526

openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

Abstract

We generalize Goodstein's theorem (Goodstein 1944) and Cichon's independence proof (Cichon 1983) to Π¹₁-CA₀ using results from (Wilken 2026). The method is generalizable to stronger notation systems that provide unique terms for ordinals and enjoy Bachmann property.

Citations

• Fundamental sequences based on localization
• Fast Goodstein Walks
• Predicatively unprovable termination of the Ackermannian Goodstein process

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