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Algebra i logika, 2022, Volume 61, Number 1, Pages 42–76
DOI: https://doi.org/10.33048/alglog.2022.61.103
(Mi al2696)
 

This article is cited in 1 scientific paper (total in 1 paper)

Index sets for classes of positive preorders

B. S. Kalmurzaevab, N. A. Bazhenovc, M. A. Torebekovab

a Al-Farabi Kazakh National University
b Kazakh-British Technical University
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (356 kB) Citations (1)
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Abstract: We study the complexity of index sets with respect to a universal computable numbering of the family of all positive preorders. Let $\leq_c$ be computable reducibility on positive preorders. For an arbitrary positive preorder $R$ such that the $R$-induced equivalence $\sim_R$ has infinitely many classes, the following results are obtained. The index set for preorders $P$ with $R\leq_c P$ is $\Sigma^0_3$-complete. A preorder $R$ is said to be self-full if the range of any computable function realizing the reduction $R\leq_c R$ intersects all $\sim_R$-classes. If $L$ is a non-self-full positive linear preorder, then the index set of preorders $P$ with $P\equiv_c L$ is $\Sigma^0_3$-complete. It is proved that the index set of self-full linear preorders is $\Pi^0_3$-complete.
Keywords: positive preorder, positive equivalence, positive linear preorder, computable reducibility, index set.
Received: 28.07.2021
Revised: 07.06.2022
Document Type: Article
UDC: 510.5
Language: Russian
Citation: B. S. Kalmurzaev, N. A. Bazhenov, M. A. Torebekova, “Index sets for classes of positive preorders”, Algebra Logika, 61:1 (2022), 42–76
Citation in format AMSBIB
\Bibitem{KalBazTor22}
\by B.~S.~Kalmurzaev, N.~A.~Bazhenov, M.~A.~Torebekova
\paper Index sets for classes of positive preorders
\jour Algebra Logika
\yr 2022
\vol 61
\issue 1
\pages 42--76
\mathnet{http://mi.mathnet.ru/al2696}
\crossref{https://doi.org/10.33048/alglog.2022.61.103}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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    Abstract page:126
    Full-text PDF :42
    References:22
    First page:6
     
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