Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies

Standard

Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies. / Bazhenov, N. A.; Mustafa, M.; San Mauro, L. et al.

In: Lobachevskii Journal of Mathematics, Vol. 41, No. 2, 01.02.2020, p. 145-150.

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

Harvard

Bazhenov, NA, Mustafa, M, San Mauro, L & Yamaleev, MM 2020, 'Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies', Lobachevskii Journal of Mathematics, vol. 41, no. 2, pp. 145-150. https://doi.org/10.1134/S199508022002002X

APA

Bazhenov, N. A., Mustafa, M., San Mauro, L., & Yamaleev, M. M. (2020). Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies. Lobachevskii Journal of Mathematics, 41(2), 145-150. https://doi.org/10.1134/S199508022002002X

Vancouver

Bazhenov NA, Mustafa M, San Mauro L, Yamaleev MM. Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies. Lobachevskii Journal of Mathematics. 2020 Feb 1;41(2):145-150. doi: 10.1134/S199508022002002X

Author

Bazhenov, N. A. ; Mustafa, M. ; San Mauro, L. et al. / Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies. In: Lobachevskii Journal of Mathematics. 2020 ; Vol. 41, No. 2. pp. 145-150.

BibTeX

@article{95d5e106c61d44258068168eec06f049,

title = "Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies",

abstract = "A standard tool for classifying the complexity of equivalence relations on ω is provided by computable reducibility. This reducibility gives rise to a rich degree structure. The paper studies equivalence relations, which (Formula presented.), where α ≥ 2 is a computable ordinal and n is a non-zero natural number. We prove that there are infinitely many pairwise incomparable minimal equivalence relations that are properly in Γ.",

keywords = "analytical hierarchy, computable reducibility, equivalence relation, hyperarithmetical hierarchy, minimal degree",

author = "Bazhenov, {N. A.} and M. Mustafa and {San Mauro}, L. and Yamaleev, {M. M.}",

year = "2020",

month = feb,

day = "1",

doi = "10.1134/S199508022002002X",

language = "English",

volume = "41",

pages = "145--150",

journal = "Lobachevskii Journal of Mathematics",

issn = "1995-0802",

publisher = "Maik Nauka Publishing / Springer SBM",

number = "2",

}

RIS

TY - JOUR

T1 - Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies

AU - Bazhenov, N. A.

AU - Mustafa, M.

AU - San Mauro, L.

AU - Yamaleev, M. M.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - A standard tool for classifying the complexity of equivalence relations on ω is provided by computable reducibility. This reducibility gives rise to a rich degree structure. The paper studies equivalence relations, which (Formula presented.), where α ≥ 2 is a computable ordinal and n is a non-zero natural number. We prove that there are infinitely many pairwise incomparable minimal equivalence relations that are properly in Γ.

AB - A standard tool for classifying the complexity of equivalence relations on ω is provided by computable reducibility. This reducibility gives rise to a rich degree structure. The paper studies equivalence relations, which (Formula presented.), where α ≥ 2 is a computable ordinal and n is a non-zero natural number. We prove that there are infinitely many pairwise incomparable minimal equivalence relations that are properly in Γ.

KW - analytical hierarchy

KW - computable reducibility

KW - equivalence relation

KW - hyperarithmetical hierarchy

KW - minimal degree

UR - http://www.scopus.com/inward/record.url?scp=85087878058&partnerID=8YFLogxK

U2 - 10.1134/S199508022002002X

DO - 10.1134/S199508022002002X

M3 - Article

AN - SCOPUS:85087878058

VL - 41

SP - 145

EP - 150

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 2

ER -

ID: 24768915