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arXiv · 2603.03994

Robinson Splitting Theorem and $\Sigma_1$ Induction

Yong Liu·Cheng Peng·Mengzhou Sun
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Abstract

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

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Yong Liu, Cheng Peng, Mengzhou Sun. 2026-03-04. Robinson Splitting Theorem and $\Sigma_1$ Induction. https://arxiv.org/abs/2603.03994

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