Failure modes for structural highness notions.
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| Title: | Failure modes for structural highness notions. |
|---|---|
| Authors: | Calvert, Wesley1 (AUTHOR), Franklin, Johanna N Y2 (AUTHOR), Turetsky, Dan3 (AUTHOR) |
| Source: | Journal of Logic & Computation. Oct2025, Vol. 35 Issue 7, p1-17. 17p. |
| Subjects: | Computable functions, Isomorphism (Mathematics), Scholarly method |
| Abstract: | In Calvert, Franklin, and Turetsky (2023, J. Symb. Log. 88, 1692–1724), we defined several classes of degrees that are high in senses related to computable structure theory. Each class of degrees is characterized by a structural feature (e.g. an isomorphism) that it can compute if such a feature exists. In this paper, we examine each of these classes and characterize them based on what they do if no such object exists. We describe, in particular, reticent, loquacious and collegiate senses of being high. These, respectively, reflect the case where a computation from the degree will give output only if the desired feature exists, the case where it will give output of some kind whether or not the feature exists, and the case where the degree will compute either the feature or the best available approximation to it. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 188960984 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Failure modes for structural highness notions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Calvert%2C+Wesley%22">Calvert, Wesley</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Franklin%2C+Johanna+N+Y%22">Franklin, Johanna N Y</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Turetsky%2C+Dan%22">Turetsky, Dan</searchLink><relatesTo>3</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Logic+%26+Computation%22">Journal of Logic & Computation</searchLink>. Oct2025, Vol. 35 Issue 7, p1-17. 17p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Computable+functions%22">Computable functions</searchLink><br /><searchLink fieldCode="DE" term="%22Isomorphism+%28Mathematics%29%22">Isomorphism (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Scholarly+method%22">Scholarly method</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In Calvert, Franklin, and Turetsky (2023, J. Symb. Log. 88, 1692–1724), we defined several classes of degrees that are high in senses related to computable structure theory. Each class of degrees is characterized by a structural feature (e.g. an isomorphism) that it can compute if such a feature exists. In this paper, we examine each of these classes and characterize them based on what they do if no such object exists. We describe, in particular, reticent, loquacious and collegiate senses of being high. These, respectively, reflect the case where a computation from the degree will give output only if the desired feature exists, the case where it will give output of some kind whether or not the feature exists, and the case where the degree will compute either the feature or the best available approximation to it. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=188960984 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1093/logcom/exaf051 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 1 Subjects: – SubjectFull: Computable functions Type: general – SubjectFull: Isomorphism (Mathematics) Type: general – SubjectFull: Scholarly method Type: general Titles: – TitleFull: Failure modes for structural highness notions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Calvert, Wesley – PersonEntity: Name: NameFull: Franklin, Johanna N Y – PersonEntity: Name: NameFull: Turetsky, Dan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 0955792X Numbering: – Type: volume Value: 35 – Type: issue Value: 7 Titles: – TitleFull: Journal of Logic & Computation Type: main |
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