Skip to main content
SpringerLink
Log in

The discontinuity of splitting in the recursively enumerable degrees

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

In this paper we examine a class of pairs of recursively enumerable degrees, which is related to the Slaman-Soare Phenomenon.

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

  • Ambos-Spies, K., Ding, D.: Discontinuity of capping in the recursively enumerable degrees and strongly nonbranching degrees. Math Log Quart40, 287–317 (1994)

    Google Scholar 

  • Ambos-Spies, K., Lachlan, A.H., Soare, R.I.: The continuity of cupping to0′. Ann Pure Appl Logic64, 195–209 (1993)

    Article  Google Scholar 

  • Ambos-Spies, K., Shore, R.A.: Undecidability and 1-types in the recursively enumerable degrees. Ann Pure Appl Logic63, 3–37 (1993)

    Article  Google Scholar 

  • Cooper, S.B.: Discontinuous phenomena and Turing definability. In: Kazan (ed.) Proceedings of the International Conference of Algebra and Analysis. Amsterdam: de Gruyter 1994

    Google Scholar 

  • Cooper, S.B., Sui, Y., Yi, X.: Minimal pairs and the Slaman-Soare phenomenon. In preparation

  • Harrington, L.A., Soare, R.I.: Games in recursion theory and continuity properties of capping degrees. In: Judah, H., Just, W., Woodin, W.H. (eds.) Set theory and the continuum, pp. 39–62. Berlin Heidelberg New York: Springer 1992

    Google Scholar 

  • Lachlan, A.H.: Lower bounds for pairs of recursively enumerable degrees. Proc London Math Soc16, 537–569 (1966)

    Google Scholar 

  • Lerman, M.: General ∀∃-decision method for degree structures. Unpublished (1993)

  • Sacks, G.E.: On the degrees less than0′. Ann Math77, 211–231 (1963)

    Google Scholar 

  • Seetapun, D.: Every recursively enumerable degree is locally noncappable. Preprint

  • Soare, R.I.: Recursively enumerable sets and degrees. Perspectives in Mathematical Logic, Omega Series. Berlin Heidelberg New York: Springer 1987

    Google Scholar 

  • Stob, M.: wtt-degrees and T-degrees of recursively enumerable sets. J Symb Logic48, 921–930 (1983)

    Google Scholar 

  • Yates, C.E.M.: A minimal pair of recursively enumerable degrees. J. Symb Logic31, 159–168 (1966)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, England, UK

    S. Barry Cooper & Xiaoding Yi

Authors
  1. S. Barry Cooper
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoding Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Preparation of this paper supported by S.E.R.C. (UK) Research Grant no. GR/H 02165, and by European network ‘Complexity, Logic and Recursion Theory’ (EC Contract No. ERBCHRXCT930415). The second author wishes to thank Alistair H. Lachlan and the University of Leeds

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cooper, S.B., Yi, X. The discontinuity of splitting in the recursively enumerable degrees. Arch Math Logic 34, 247–256 (1995). https://doi.org/10.1007/BF01469381

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01469381

Keywords

Search

Navigation