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 |
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Pages (from-to) | 145-150 |
Number of pages | 6 |
Journal | Lobachevskii Journal of Mathematics |
Volume | 41 |
Issue number | 2 |
DOIs | |
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