@article{ef7baf67a7134dd5aceb8b0457537cb4,
title = "Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies",
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.",
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.}",
note = "Funding Information: 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 Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
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 = "Kazanskii Gosudarstvennyi Universitet/Kazan State University",
number = "2",
}