The characterization of Weihrauch reducibility in systems containing E-PA$^{\omega}$ + QF-AC$^{0,0}$

Abstract

We characterize Weihrauch reducibility in E-PA$^{\omega}$ + QF-AC$^{0,0}$ and all systems containing it by the provability in a linear variant of the same calculus using modifications of G\"odel's Dialectica interpretation that incorporate ideas from linear logic, nonstandard arithmetic, higher-order computability, and phase semantics.