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Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 107–121 (Mi smj2845)  

This article is cited in 2 scientific papers (total in 2 papers)

Sufficient conditions for the existence of $\mathbf0'$-limitwise monotonic functions for computable $\eta$-like linear orders

M. V. Zubkov

Kazan (Volga Region) Federal University, Lobachevskiĭ Institute of Mathematics and Mechanics, Kazan, Russia

Abstract: We find new sufficient conditions for the existence of a $\mathbf0'$-limitwise monotonic function defining the order for a computable $\eta$-like linear order $\mathscr L$, i.e., of a function $G$ such that $\mathscr L\cong\sum_{q\in\mathbb Q}G(q)$. Namely, we define the notions of left local maximal block and right local maximal block and prove that if the sizes of these blocks in a computable $\eta$-like linear order $\mathscr L$ are bounded then there is a $\mathbf0'$-limitwise monotonic function $G$ with $\mathscr L\cong\sum_{q\in\mathbb Q}G(q)$.

Keywords: computable linear order, $\eta$-like linear order, $\mathbf0'$–limitwise monotonic function.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-41-02502
15-01-08252
15-31-20607
The author was partially supported by the Russian Foundation for Basic Research (Grants 15-41-02502, 15-01-08252, and 15-31-20607).


DOI: https://doi.org/10.17377/smzh.2017.58.112

Full text: PDF file (370 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:1, 80–90

Bibliographic databases:

UDC: 510.53+512.562
MSC: 35R30
Received: 19.02.2016

Citation: M. V. Zubkov, “Sufficient conditions for the existence of $\mathbf0'$-limitwise monotonic functions for computable $\eta$-like linear orders”, Sibirsk. Mat. Zh., 58:1 (2017), 107–121; Siberian Math. J., 58:1 (2017), 80–90

Citation in format AMSBIB
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\by M.~V.~Zubkov
\paper Sufficient conditions for the existence of $\mathbf0'$-limitwise monotonic functions for computable $\eta$-like linear orders
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 1
\pages 107--121
\mathnet{http://mi.mathnet.ru/smj2845}
\crossref{https://doi.org/10.17377/smzh.2017.58.112}
\elib{http://elibrary.ru/item.asp?id=29159908}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 1
\pages 80--90
\crossref{https://doi.org/10.1134/S0037446617010128}
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\elib{http://elibrary.ru/item.asp?id=29490178}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014728825}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Morozov, “A computably enumerable partial ordering without computably enumerable maximal chains and antichains”, Siberian Math. J., 59:3 (2018), 463–469  mathnet  crossref  crossref  isi  elib
    2. G. Wu, M. Zubkov, “The Kierstead's conjecture and limitwise monotonic functions”, Ann. Pure Appl. Log., 169:6 (2018), 467–486  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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