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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 4, Pages 3–9 (Mi ivm6720)  

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

Isolated 2-computably enumerable $Q$-degrees

I. I. Batyrshin

Chair of Algebra and Mathematical Logic, Kazan State University, Kazan, Russia
Full-text PDF (188 kB) Citations (3)
References:
Abstract: We demonstrate that for every pair of computably enumerable degrees $\mathbf a<_\mathbf Q\mathbf b$ there exists a properly 2-computably enumerable degree $\mathbf d$, $\mathbf a<_\mathbf Q\mathbf d<_\mathbf Q\mathbf b$, such that $\mathbf a$ isolates $\mathbf d$ from below and $\mathbf b$ isolates $\mathbf d$ from above. As a corollary we prove that there exists a 2-computably enumerable degree which is $Q$-incomparable with any nontrivial (i.e., different from $\boldsymbol0$ and $\boldsymbol0'$) computably enumerable degree, and that every nontrivial computably enumerable degree isolates some 2-computably enumerable degree from below and some 2-computably enumerable degree from above.
Keywords: computably enumerable sets, quasi-reducibility, 2-computably enumerable sets, isolated degrees.
Received: 03.03.2008
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 4, Pages 1–6
DOI: https://doi.org/10.3103/S1066369X10040018
Bibliographic databases:
UDC: 510.532
Language: Russian
Citation: I. I. Batyrshin, “Isolated 2-computably enumerable $Q$-degrees”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 4, 3–9; Russian Math. (Iz. VUZ), 54:4 (2010), 1–6
Citation in format AMSBIB
\Bibitem{Bat10}
\by I.~I.~Batyrshin
\paper Isolated 2-computably enumerable $Q$-degrees
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 4
\pages 3--9
\mathnet{http://mi.mathnet.ru/ivm6720}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2779407}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 4
\pages 1--6
\crossref{https://doi.org/10.3103/S1066369X10040018}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649623512}
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  • https://www.mathnet.ru/eng/ivm/y2010/i4/p3
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Abstract page:369
    Full-text PDF :68
    References:54
    First page:6
     
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