Skip to main content
SpringerLink
Log in

The last question on recursively enumerablem-degrees

  • Published:
Algebra and Logic Aims and scope

Abstract

The theory of the r.e. m-degrees has the same computational complexity as true arithmetic. In fact, it is possible to define without parameters a standard model of arithmetic in this degree structure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. H. Lachlan, “Recursively enumerable many-one degrees,”Algebra Logika,11, No. 3, 326–358 (1972).

    Google Scholar 

  2. A. Nies,Undecidable Fragments of Elementary Theories, preprint, to appear.

  3. A. N. Degtev, “Several results on uppersemilattices andm-degrees,”Algebra Logika,18, No. 6, 664–679 (1979).

    Google Scholar 

  4. S. D. Denisov, “The structure of the uppersemilattice of recursively enumerablem-degrees and related questions,”Algebra Logika,17, No. 6, 643–683 (1978).

    Google Scholar 

  5. A. Nerode and R. Shore, “Second-order logic and first-order theory of reducibility orderings,” in:Kleene Symposium, Barwise et al. (eds.), North Holland (1978), pp. 181–200.

  6. L. Harrington and S. Shelah, “The undecidability of the recursively enumerable degrees (research announcement),”Bull. Am. Math. Soc.,6, No. 1, 79–80 (1982).

    Google Scholar 

  7. R. Shore, “The theory of the degrees below Ø′,”J. London Math. Soc.,24, No. 1, 1–14 (1981).

    Google Scholar 

  8. A. Nies and R. Shore, “Interpreting arithmetic in the theory of the r.e. truth-table degrees,” to appear inAnn. Pure Appl. Logic.

  9. P. Odifreddi,Classical Recursion Theory, Vol. 1, North Holland (1989).

  10. A. Nies,The Model Theory of the Structure of Recursively Enumerable Many-One Degrees, preprint, to appear.

  11. K. Ambos-Spies, A. Nies, and R. Shore, “The theory of the r.e. weak truth-table degrees is undecidable,”J. Symb. Logic,57, No. 3, 864–874 (1992).

    Google Scholar 

  12. Yu. L. Ershov and I. A. Lavrov, “The uppersemilatticeL(γ),”Algebra Logika,12, No. 2, 167–189 (1973).

    Google Scholar 

  13. R. I. Scare,Recursively Enumerable Sets and Degree, Springer Verlag, Berlin (1987).

    Google Scholar 

Download references

Authors
  1. A. Nies
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromAlgebra i Logika, Vol. 33, No. 5, pp. 550–563, September–October, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nies, A. The last question on recursively enumerablem-degrees. Algebr Logic 33, 307–314 (1994). https://doi.org/10.1007/BF00739571

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00739571

Keywords

Search

Navigation