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The Structure of Computable Reducibility on Preorders. / Alish, D. B.; Bazhenov, N. A.

In: Algebra and Logic, Vol. 64, No. 4, 09.2025, p. 219–228.

Research output: Contribution to journal › Article › peer-review

Harvard

Alish, DB & Bazhenov, NA 2025, 'The Structure of Computable Reducibility on Preorders', Algebra and Logic, vol. 64, no. 4, pp. 219–228. https://doi.org/10.1007/s10469-026-09827-3

APA

Alish, D. B., & Bazhenov, N. A. (2025). The Structure of Computable Reducibility on Preorders. Algebra and Logic, 64(4), 219–228. https://doi.org/10.1007/s10469-026-09827-3

Vancouver

Alish DB, Bazhenov NA. The Structure of Computable Reducibility on Preorders. Algebra and Logic. 2025 Sept;64(4):219–228. doi: 10.1007/s10469-026-09827-3

Author

Alish, D. B. ; Bazhenov, N. A. / The Structure of Computable Reducibility on Preorders. In: Algebra and Logic. 2025 ; Vol. 64, No. 4. pp. 219–228.

BibTeX

@article{001760deb7004b4cb2ea3993626b4d2a,
title = "The Structure of Computable Reducibility on Preorders",
abstract = "We investigate degree structures induced by computable reducibility ≤c on binary relations having domain ω. We prove that for each of the following structures induced by ≤c, its first-order theory is recursively isomorphic to the second-order arithmetic: the structure Pr of all preorders, and the structure LP of all linear preorders.",
keywords = "computable reducibility, linear preorder, preorder, second-order arithmetic",
author = "Alish, {D. B.} and Bazhenov, {N. A.}",
note = "Alish, D.B., Bazhenov, N.A. The Structure of Computable Reducibility on Preorders. Algebra Logic 64, 219–228 (2025). https://doi.org/10.1007/s10469-026-09827-3",
year = "2025",
month = sep,
doi = "10.1007/s10469-026-09827-3",
language = "English",
volume = "64",
pages = "219–228",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "4",

}

RIS

TY - JOUR

T1 - The Structure of Computable Reducibility on Preorders

AU - Alish, D. B.

AU - Bazhenov, N. A.

N1 - Alish, D.B., Bazhenov, N.A. The Structure of Computable Reducibility on Preorders. Algebra Logic 64, 219–228 (2025). https://doi.org/10.1007/s10469-026-09827-3

PY - 2025/9

Y1 - 2025/9

N2 - We investigate degree structures induced by computable reducibility ≤c on binary relations having domain ω. We prove that for each of the following structures induced by ≤c, its first-order theory is recursively isomorphic to the second-order arithmetic: the structure Pr of all preorders, and the structure LP of all linear preorders.

AB - We investigate degree structures induced by computable reducibility ≤c on binary relations having domain ω. We prove that for each of the following structures induced by ≤c, its first-order theory is recursively isomorphic to the second-order arithmetic: the structure Pr of all preorders, and the structure LP of all linear preorders.

KW - computable reducibility

KW - linear preorder

KW - preorder

KW - second-order arithmetic

UR - https://www.scopus.com/pages/publications/105044319411

UR - https://www.mendeley.com/catalogue/8292e947-52bf-324d-9259-201f5202ece0/

U2 - 10.1007/s10469-026-09827-3

DO - 10.1007/s10469-026-09827-3

M3 - Article

VL - 64

SP - 219

EP - 228

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 4

ER -

ID: 80915405