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The Existence of Primitive Recursive Structures. / Alaev, Pavel E.

Crossroads of Computability and Logic: Insights, Inspirations, and Innovations. Vol. 15764 2025. p. 119-132.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Alaev, PE 2025, The Existence of Primitive Recursive Structures. in Crossroads of Computability and Logic: Insights, Inspirations, and Innovations. vol. 15764, pp. 119-132, 21 Conference on Computability in Europe, 01.01.2025. https://doi.org/10.1007/978-3-031-95908-0_9

APA

Alaev, P. E. (2025). The Existence of Primitive Recursive Structures. In Crossroads of Computability and Logic: Insights, Inspirations, and Innovations (Vol. 15764, pp. 119-132) https://doi.org/10.1007/978-3-031-95908-0_9

Vancouver

Alaev PE. The Existence of Primitive Recursive Structures. In Crossroads of Computability and Logic: Insights, Inspirations, and Innovations. Vol. 15764. 2025. p. 119-132 doi: 10.1007/978-3-031-95908-0_9

Author

Alaev, Pavel E. / The Existence of Primitive Recursive Structures. Crossroads of Computability and Logic: Insights, Inspirations, and Innovations. Vol. 15764 2025. pp. 119-132

BibTeX

@inbook{f9bfa62eae7b4d41892cc4a6beb2ad36,
title = "The Existence of Primitive Recursive Structures",
abstract = "We suggest a general, relatively simple criterion for the existence of a primitive recursive (p.r.) or punctual presentation of a given structure. As an example, we prove that every computable Abelian group with a computably enumerable linear basis has a p.r. presentation. A series of other examples is found.",
keywords = "computability, computable structure, punctual structure, primitive recursive structure, Abelian group, partial ordering, Boolean algebra",
author = "Alaev, {Pavel E.}",
note = "The research was supported by grant of the Russian Science Foundation No. 23-11-00170, https://rscf.ru/project/23-11-00170.; 21 Conference on Computability in Europe, CiE ; Conference date: 01-01-2025",
year = "2025",
month = jun,
day = "20",
doi = "10.1007/978-3-031-95908-0_9",
language = "English",
isbn = "9783031959073",
volume = "15764",
publisher = "Lecture Notes in Computer Science",
pages = "119--132",
booktitle = "Crossroads of Computability and Logic: Insights, Inspirations, and Innovations",

}

RIS

TY - CHAP

T1 - The Existence of Primitive Recursive Structures

AU - Alaev, Pavel E.

N1 - Conference code: 21

PY - 2025/6/20

Y1 - 2025/6/20

N2 - We suggest a general, relatively simple criterion for the existence of a primitive recursive (p.r.) or punctual presentation of a given structure. As an example, we prove that every computable Abelian group with a computably enumerable linear basis has a p.r. presentation. A series of other examples is found.

AB - We suggest a general, relatively simple criterion for the existence of a primitive recursive (p.r.) or punctual presentation of a given structure. As an example, we prove that every computable Abelian group with a computably enumerable linear basis has a p.r. presentation. A series of other examples is found.

KW - computability

KW - computable structure

KW - punctual structure

KW - primitive recursive structure

KW - Abelian group

KW - partial ordering

KW - Boolean algebra

UR - https://www.mendeley.com/catalogue/40a2bc22-3900-3f96-bc93-c133742b2c41/

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105009320294&origin=inward

U2 - 10.1007/978-3-031-95908-0_9

DO - 10.1007/978-3-031-95908-0_9

M3 - Chapter

SN - 9783031959073

VL - 15764

SP - 119

EP - 132

BT - Crossroads of Computability and Logic: Insights, Inspirations, and Innovations

T2 - 21 Conference on Computability in Europe

Y2 - 1 January 2025

ER -

ID: 68292698