Algebra and Logic

, Volume 36, Issue 6, pp 359–369 | Cite as

Generalized computable numerations and nontrivial rogers semilattices

  • S. S. Goncharov
  • A. Sorbi


We outline the general approach to the notion of a computable numeration in the frames of which computable numerations, of families of arithmetic sets are studied.


Recursive Function Existential Quantifier Computable Numberings Algorithm Theory Recursive Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Rogers,Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).zbMATHGoogle Scholar
  2. 2.
    Yu. L. Ershov,Numeration Theory [in Russian], Nauka, Moscow (1977).Google Scholar
  3. 3.
    Yu. L. Ershov,Decidability Problems and Constructive Models [in Russian], Nauka, Moscow (1980).Google Scholar
  4. 4.
    A. I. Mal'tsev,Algorithms and Recursive Functions [in Russian], Nauka, Moscow (1965).Google Scholar
  5. 5.
    S. C. Kleene,Introduction to Metamathematics, Princeton, N. J. (1952).Google Scholar
  6. 6.
    A. N. Kolmogorov and V. A. Uspenskii, “Defining an Algorithm,”Usp. Mat. Nauk, 13, No. 4 (82), 2–28 (1958).Google Scholar
  7. 7.
    V. A. Uspenskii, “Systems of denumerable sets and their numerations,”Dok. Akad. Nauk SSSR, 105, No. 6, 1155–1158 (1955).Google Scholar
  8. 8.
    V. A. Uspenskii,Lectures on Computable Functions [in Russian], Fizmatgiz, Moscow (1960).Google Scholar
  9. 9.
    H. Rogers, “Gödel numberings of partial recursive functions,”J. Symb. Log., 23, No. 3, 331–341 (1958).CrossRefGoogle Scholar
  10. 10.
    R. F. Friedberg, “Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplication,”J. Symb. Log., 23, No. 3, 309–316 (1958).CrossRefGoogle Scholar
  11. 11.
    I. A. Lavrov, “Computable numberings,” inProc. 5th Int. Congr. Logic, Methodology and Philosophy of Science, Part 1, Reidel, Dordrecht (1977), pp. 195–206.Google Scholar
  12. 12.
    M. B. Pour-El, “Gödel numberings versus Friedberg numberings,”Proc. Am. Math. Soc., 15, No. 2, 252–256 (1964).zbMATHCrossRefGoogle Scholar
  13. 13.
    M. B. Pour-El and H. Putnam, “Recursively enumerable classes and their applications to sequence of formal theories,”Arch. Math. Log. Gr., 8, 104–121 (1965).zbMATHCrossRefGoogle Scholar
  14. 14.
    S. S. Goncharov, “The problem of the number of non-autoequivalent constructivizations,”Dokl. Akad. Nauk SSSR, 251, No. 2, 271–274 (1980).Google Scholar
  15. 15.
    A. I. Maltsev, “Toward a theory of computable families of objects,”Algebra Logika, 3, No. 4, 5–31 (1964).Google Scholar
  16. 16.
    S. S. Goncharov, A. Yakhnis and V. Yakhnis, “Some effectively infinite classes of enumerations,”Ann. Pure Appl. Log., 60, 207–235 (1993).zbMATHCrossRefGoogle Scholar
  17. 17.
    Yu. L. Ershov,Definability and Computability [in Russian], Nauch. Kniga, Novosibirsk (1996).Google Scholar
  18. 18.
    A. B. Khutoretskii, “On the cardinality of the upper semilattice of computable numerations,”Algebra Logika, 10, No. 5, 561–569 (1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • S. S. Goncharov
  • A. Sorbi

There are no affiliations available

Personalised recommendations