Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies

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

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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 languageEnglish
Pages (from-to)145-150
Number of pages6
JournalLobachevskii Journal of Mathematics
Volume41
Issue number2
DOIs
Publication statusPublished - 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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