Lipschitz and Wadge binary games in second order arithmetic

Abstract

We present a detailed formalization of Lipschitz and Wadge games in the context of second order arithmetic and we investigate the logical strength of Lipschitz and Wadge determinacy, and the tightly related Semi-Linear Ordering principle, for the first levels of the Hausdorff difference hierarchy in the Cantor space. As a result, we obtain characterizations of ${\mathrm{WKL}}_0$ and ${\mathrm{ACA}}_0$ in terms of these determinacy principles.