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

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

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

Keywords

analytical hierarchy
computable reducibility
equivalence relation
hyperarithmetical hierarchy
minimal degree

ASJC Scopus subject areas

Mathematics(all)

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