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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2010, Volume 10, Issue 4, Pages 125–132 (Mi vngu63)  

This article is cited in 3 scientific papers (total in 3 papers)

Some Properties of Numberings in Various Levels in Ershov's Hierarchy

S. S. Ospichev

Novosibirsk State University

Abstract: There was proved, that there no $\Delta^{-1}_{a}$-computable numbering of family of all $\Delta^{-1}_{a}$-sets, $a$ is constructive ordinal. Also there was proved, that there is minimal $\omega$-computable numbering of family of all sets from $\bigcup\limits_{k\in\omega}\Sigma_{k}^{-1}$.

Keywords: computable numbering, friedberg numbering, Ershov's hierarchy.

Full text: PDF file (229 kB)
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English version:
Journal of Mathematical Sciences, 2013, 188:4, 441–448

Document Type: Article
UDC: 510.10+510.57
Received: 22.01.2010

Citation: S. S. Ospichev, “Some Properties of Numberings in Various Levels in Ershov's Hierarchy”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 10:4 (2010), 125–132; J. Math. Sci., 188:4 (2013), 441–448

Citation in format AMSBIB
\Bibitem{Osp10}
\by S.~S.~Ospichev
\paper Some Properties of Numberings in Various Levels in Ershov's Hierarchy
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2010
\vol 10
\issue 4
\pages 125--132
\mathnet{http://mi.mathnet.ru/vngu63}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 188
\issue 4
\pages 441--448
\crossref{https://doi.org/10.1007/s10958-012-1140-5}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. S. Ospichev, “Computable families of sets in Ershov hierarchy without principal numberings”, J. Math. Sci., 215:4 (2016), 529–536  mathnet  crossref
    2. S. S. Ospichev, “Friedberg numberings in the Ershov hierarchy”, Algebra and Logic, 54:4 (2015), 283–295  mathnet  crossref  crossref  mathscinet  isi
    3. N. A. Bazhenov, “The branching theorem and computable categoricity in the Ershov hierarchy”, Algebra and Logic, 54:2 (2015), 91–104  mathnet  crossref  crossref  mathscinet  isi
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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