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Article . 2023
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On the first-order parts of problems in the Weihrauch degrees

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 31 Jan 2024Embargo end date: 01 Jan 2023Publisher:SAGE PublicationsJournal:Computability (issn: 2211-3568, eissn: 2211-3576, Copyright policy )Funded by:NSF | FRG: Collaborative Resear...
Authors: Dzhafarov, Damir D.; Solomon, Reed; Yokoyama, Keita;

doi: 10.3233/com-230446 , 10.48550/arxiv.2301.12733

arXiv: 2301.12733

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

Abstract

We introduce the notion of the first-order part of a problem in the Weihrauch degrees. Informally, the first-order part of a problem P is the strongest problem with codomaixn ω that is Weihrauch reducible to 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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Keywords

FOS: Mathematics, Mathematics - Logic, Computability and recursion theory, Logic (math.LO)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Top 10%
Average
Average
Green