Robinson Splitting Theorem and $\hat{I}{\pounds }_1$ Induction

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 ${\mathrm{P}}^{-}+\mathrm{I}\hat{I}{\pounds }_1$, with lowness replaced by superlowness.