Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies

N. A. Bazhenov; M. Mustafa; L. San Mauro; M. M. Yamaleev

doi:10.1134/S199508022002002X

Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies

N. A. Bazhenov
, M. Mustafa
, L. San Mauro
, M. M. Yamaleev

RAS - Sobolev Institute of Mathematics, Siberian Branch
Novosibirsk State University
Vienna University of Technology
Kazan Volga Region Federal University

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

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	145-150
Number of pages	6
Journal	Lobachevskii Journal of Mathematics
Volume	41
Issue number	2
DOIs	https://doi.org/10.1134/S199508022002002X
Publication status	Published - Feb 1 2020

Funding

The work was supported by Nazarbayev University Faculty Development Competitive Research Grants N090118FD5342. Bazhenov was supported by the grant of the President of the Russian Federation (No. MK-1214.2019.1). San Mauro was supported by the Austrian Science Fund FWF, project M 2461. Yamaleev was supported by the Russian Science Foundation, project No. 18-11-00028. ACKNOWLEDGMENTS

Keywords

analytical hierarchy
computable reducibility
equivalence relation
hyperarithmetical hierarchy
minimal degree

ASJC Scopus subject areas

General Mathematics

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10.1134/S199508022002002X

Cite this

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abstract = "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.",

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N2 - 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.

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KW - equivalence relation

KW - hyperarithmetical hierarchy

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Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies

Abstract

Funding

Keywords

ASJC Scopus subject areas

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