English

Generalizing Goodstein's theorem and Cichon's independence proof

Logic 2026-05-06 v3

Abstract

We generalize Goodstein's theorem (Goodstein 1944) and Cichon's independence proof (Cichon 1983) to Π11CA0\Pi^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.

Keywords

Cite

@article{arxiv.2511.04526,
  title  = {Generalizing Goodstein's theorem and Cichon's independence proof},
  author = {Gunnar Wilken},
  journal= {arXiv preprint arXiv:2511.04526},
  year   = {2026}
}

Comments

Major revision and completion of all proofs

R2 v1 2026-07-01T07:24:49.636Z