Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies

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

Research output: Contribution to journalArticlepeer-review


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
Issue number2
Publication statusPublished - Feb 1 2020


  • analytical hierarchy
  • computable reducibility
  • equivalence relation
  • hyperarithmetical hierarchy
  • minimal degree

ASJC Scopus subject areas

  • Mathematics(all)

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