English

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

Logic 2023-01-31 v1

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 P\mathsf{P} is the strongest problem with codomaixn ω\omega that is Weihrauch reducible to P\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.

Keywords

Cite

@article{arxiv.2301.12733,
  title  = {On the first-order parts of problems in the Weihrauch degrees},
  author = {Damir D. Dzhafarov and Reed Solomon and Keita Yokoyama},
  journal= {arXiv preprint arXiv:2301.12733},
  year   = {2023}
}