Siberian Mathematical Journal

, Volume 49, Issue 5, pp 780–783 | Cite as

Some remarks on completion of numberings

  • S. A. BadaevEmail author
  • S. S. Goncharov
  • A. Sorbi


We present some examples and constructions in the theory of complete numberings and completions of numberings that partially answer a few questions of [1].


numbering computability complete numbering Rogers semilattice computability with an oracle arithmetical numbering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Badaev S., Goncharov S., and Sorbi A., “Completeness and universality of arithmetical numberings,” in: Computability and Models, Kluwer Academic Publishers, New York, 2003, pp. 11–44.Google Scholar
  2. 2.
    Mal’tsev A. I., “Sets with complete numberings,” Algebra and Logic, 2, No. 2, 353–378 (1963).Google Scholar
  3. 3.
    Ershov Yu. L., Theory of Numberings [in Russian], Nauka, Moscow (1977).Google Scholar
  4. 4.
    Ershov Yu. L., “On inseparable pairs,” Algebra and Logic, 9, No. 6, 396–399 (1970).zbMATHCrossRefGoogle Scholar
  5. 5.
    Lachlan A. H., “Recursively enumerable many-one degrees,” Algebra i Logika, 11, No. 3, 326–358 (1972).MathSciNetGoogle Scholar
  6. 6.
    Lachlan A. H., “Standard classes of recursively enumerable sets,” Z. Math. Logik Grundlag. Math., 10, No. 1, 23–42 (1964).zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Al-Farabi Kazakhstan National UniversityAlmatyKazakhstan
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia
  3. 3.Dipartimento di Scienze Matematiche ed Informatiche “Roberto Magari”SienaItaly

Personalised recommendations