The strong weak truth table (sw) reducibility was suggested by Downey, Hirschfeldt and LaForte as a measure of relative randomness. In this paper, in order to discuss the structure of sw-degrees further, we introduce the definition of sw-cuppable for c.e. reals. For c.e reals, it is natural to conclude that there exist sw-cuppable c.e. reals. The main result of this paper is that there exists an sw-cuppable strongly c.e. real.


Lower Position Winning Strategy Kolmogorov Complexity Decimal Point Consecutive Stage 
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  1. 1.
    Downey, R.G., Hirschfeldt, D.: Randomness and reducibility. Springer-Verlag Monographs in Computer Science. In Preparation.Google Scholar
  2. 2.
    Soare, R.I.: Recursively Enumerable Sets and Degrees. Springer, Berlin (1987)Google Scholar
  3. 3.
    Solovay, R.M.: Draft of a paper (or series of papers) on chaitin’s work... done for the most part during the period of Sept.-Dec. 1974 (May 1975), unpublished manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 215 pages.Google Scholar
  4. 4.
    Solovay, R.M.: On random r.e. sets. In: Arruda, A., Da Costa, N., Chuaqui, R. (eds.) Non-Classical Logics, Model Theory, and Computability. Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, July 11-17, 1976. Studies in Logic and the Foundations of Mathematics, vol. 89, pp. 283–307. North-Holland, Amsterdam (1977)Google Scholar
  5. 5.
    Yu, L., Ding, D.: There is no SW-complete c.e. real. J. Symbolic Logic 69(4), 1163–1170 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Barmpalias, G., Lewis, A.E.: A c.e. real that cannot be SW-computed by any Ω number. Notre Dame J. Formal Logic 47(2), 197–209 (2006)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Yun Fan
    • 1
    • 2
  1. 1.Department of Mathematics, Nanjing UniversityChina
  2. 2.Department of Mathematics, Southeast UniversityChina

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