English

Robinson Splitting Theorem and $\Sigma_1$ Induction

Logic 2026-03-05 v1

Abstract

The Robinson Splitting Theorem states that a c.e. degree b\mathbf{b} splits over any low c.e. degree c<b\mathbf{c}<\mathbf{b}. We prove that a weaker version of this theorem holds in models of P+IΣ1\mathrm{P}^-+\mathrm{I}\Sigma_1, with lowness replaced by superlowness.

Keywords

Cite

@article{arxiv.2603.03994,
  title  = {Robinson Splitting Theorem and $\Sigma_1$ Induction},
  author = {Yong Liu and Cheng Peng and Mengzhou Sun},
  journal= {arXiv preprint arXiv:2603.03994},
  year   = {2026}
}
R2 v1 2026-07-01T11:02:54.605Z