Cordón-Franco, AndrésLara-Martín, F. FélixLoureiro, Manuel José Simões2023Cordón-Franco , A , Lara-Martín , F F & Loureiro , M J S 2023 , ' Lipschitz and Wadge binary games in second order arithmetic ' , Default journal .1646-3730Annals of Pure and Applied LogicWe 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 WKL0 and ACA0 in terms of these determinacy principles. Keywords: Reverse mathematics, Determinacy, Wadge games, Semilinear Ordering principleapplication/pdfengopenAccessMATEMÁTICALÓGICA MATEMÁTICATEORIA DOS CONJUNTOSMATHEMATICSMATHEMATICAL LOGICSET THEORY