Degrees of incomputability, realizability and constructive reverse mathematics

Abstract

There is a way of assigning a realizability notion to each degree of incomputability. In our setting, we make use of Weihrauch degrees (degrees of incomputability/discontinuity of partial multi-valued functions) to obtain Lifschitz-like relative realizability predicates. In this note, we present sample examples on how to lift some separation results on Weihrauch degrees to those over intuitionistic Zermelo-Fraenkel set theory $\mathbf{IZF}$.

References in corpus (3)

• Constructive Reverse Mathematics
• A Galois connection between Turing jumps and limits
• Wadge-like degrees of Borel bqo-valued functions