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Algebra Logika, 2002, Volume 41, Number 5, Pages 568–584 (Mi al197)  

This article is cited in 6 scientific papers (total in 6 papers)

Decidable Computable $\mathbb A$-Numberings

V. G. Puzarenko

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The article deals in the numbering theory for admissible sets, brought in sight in [1]. For models of two special classes, we resolve the problem of there being 1-1 computable numberings of the families of all computable sets and of all computable functions. In proofs, for the former case the role of finite objects is played by syntactic constructions, and for the latter – by finite subsets on hereditarily finite superstructures.

Keywords: admissible set, numbering

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English version:
Algebra and Logic, 2002, 41:5, 314–322

Bibliographic databases:

UDC: 510.5
Received: 29.10.2000
Revised: 28.09.2001

Citation: V. G. Puzarenko, “Decidable Computable $\mathbb A$-Numberings”, Algebra Logika, 41:5 (2002), 568–584; Algebra and Logic, 41:5 (2002), 314–322

Citation in format AMSBIB
\Bibitem{Puz02}
\by V.~G.~Puzarenko
\paper Decidable Computable $\mathbb A$-Numberings
\jour Algebra Logika
\yr 2002
\vol 41
\issue 5
\pages 568--584
\mathnet{http://mi.mathnet.ru/al197}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1953180}
\zmath{https://zbmath.org/?q=an:1008.03028}
\transl
\jour Algebra and Logic
\yr 2002
\vol 41
\issue 5
\pages 314--322
\crossref{https://doi.org/10.1023/A:1020931804401}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-15044356067}


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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. V. G. Puzarenko, “Computability in special models”, Siberian Math. J., 46:1 (2005), 148–165  mathnet  crossref  mathscinet  zmath  isi
    2. V. G. Puzarenko, “Countably categorical theories”, Algebra and Logic, 51:3 (2012), 241–258  mathnet  crossref  mathscinet  zmath  isi
    3. I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrahmanov, “Partial decidable presentations in hyperarithmetic”, Siberian Math. J., 60:3 (2019), 464–471  mathnet  crossref  crossref  isi  elib
    4. I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrakhmanov, “Computable positive and Friedberg numberings in hyperarithmetic”, Algebra and Logic, 59:1 (2020), 46–58  mathnet  crossref  crossref  isi
    5. I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrakhmanov, “Pozitivnye numeratsii v dopustimykh mnozhestvakh”, Sib. matem. zhurn., 61:3 (2020), 607–621  mathnet  crossref
    6. I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrahmanov, “Semidecidable numberings in admissible sets”, Algebra and Logic, 59:3 (2020), 273–277  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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