Reverse mathematics and colorings of hypergraphs

Abstract

Working in subsystems of second order arithmetic, we formulate several representations for hypergraphs. We then prove the equivalence of various vertex coloring theorems to ${\mathsf{WKL}}_0$, ${\mathsf{ACA}}_0$ and ${\Pi }_1^1$-${\mathsf{CA}}_0$.

Preprint info in leading footnote updated