On the strength of Ramsey's theorem without Σ1‐induction
Keita Yokoyama · Mathematical logic quarterly · 2013
Abstract In this paper, we show that\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathsf {\mathrm {WKL_0}^{*}}}+{\mathrm{RT}}^{n}_{k}$\end{document} is a\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\Pi ^{0}_{2}$\end{document} ‐conservative extension of BΣ1+ exp, thus it does not imply IΣ1.