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arXiv · 2301.12733

On the first-order parts of problems in the Weihrauch degrees

Damir D. Dzhafarov·Reed Solomon·Keita Yokoyama
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Abstract

We introduce the notion of the \emph{first-order part} of a problem in the Weihrauch degrees. Informally, the first-order part of a problem $\mathsf{P}$ is the strongest problem with codomaixn $\omega$ that is Weihrauch reducible to $\mathsf{P}$. We show that the first-order part is always well-defined, examine some of the basic properties of this notion, and characterize the first-order parts of several well-known problems from the literature.

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Damir D. Dzhafarov, Reed Solomon, Keita Yokoyama. 2023-01-30. On the first-order parts of problems in the Weihrauch degrees. https://arxiv.org/abs/2301.12733

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