Degrees of incomputability, realizability and constructive reverse mathematics

Takayuki Kihara

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arXiv · 2002.10712

Degrees of incomputability, realizability and constructive reverse mathematics

Takayuki Kihara

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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 ${\bf IZF}$.

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Takayuki Kihara. 2020-02-25. Degrees of incomputability, realizability and constructive reverse mathematics. https://arxiv.org/abs/2002.10712

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