Genericity for recursively enumerable sets

  • Carl G. JockuschJr.
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1141)


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  1. [1]
    K. Ambos-Spies, On the structure of the recursively enumerable degrees, Dissertation, University of Munich, 1980.Google Scholar
  2. [2]
    K. Ambos-Spies, C. Jockusch, R. A. Shore, and R. I. Soare, An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees, Trans. Amer. Math. Soc. 281 (1984), 109–128.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    K. Ambos-Spies, On pairs of recursively enumerable degrees, Trans. Amer. Math. Soc. 283 (1984), 507–531.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    K. Ambos-Spies, Cupping and noncapping in the r.e. weak truth table and Turing degrees, Archiv für Math. Logik und Grundlagen der Math., to appear.Google Scholar
  5. [5]
    M. Bickford and C. F. Mills, Lowness properties of r.e. sets, to appearGoogle Scholar
  6. [6]
    R. Epstein, Degrees of unsolvability: Structure and theory, Lecture Notes in Mathematics. vol. 759. Springer Verlag, Berlin, Heidelberg, New York (1980).Google Scholar
  7. [7]
    M. Ingrassia, P-genericity for recursively enumerable sets, Doctoral Dissertation, University of Illinois at Urbana-Champaign, 1981Google Scholar
  8. [8]
    M. Ingrassia, P-generic r.e. degrees are dense, to appearGoogle Scholar
  9. [9]
    C. Jockusch, Degrees of generic sets, in Recursion Theory, its Generalisations and Applications, ed. by F. R. Drake and S. S. Wainer, Cambridge University Press, Cambridge (1980), 110–139.CrossRefGoogle Scholar
  10. [10]
    C. Jockusch and D. Posner, Double jumps of minimal degrees, J. Symbolic Logic 43 (1978), 715–724.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    C. Jockusch, Three easy constructions of recursively enumerable sets, in Logic Year 1979–80 (Lecture Notes in Mathematics, 859) ed. by M. Lerman, J. H. Schmerl, and R. I. Soare, Springer Verlag, Berlin, Heidelberg, New York (1981), 83–91.Google Scholar
  12. [12]
    A. H. Lachlan, Lower bounds for pairs of recursively enumerable degrees, Proc. London Math. Soc. 16 (1966), 537–569.MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    W. Maass, R. A. Shore, and M. Stob, Splitting properties and jump classes, Israel J. Math 39 (1981), 210–224.MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    W. Maass, Recursively enumerable generic sets, J. Symbolic Logic 47 (1982), 809–823.MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    W. Maass, Variations on promptly simple sets, to appear in J. Symbolic Logic.Google Scholar
  16. [16]
    J. Mohrherr, A refinement of lown and highn for the r.e. degrees, Z. Math. Logik und Grundlagen Math., to appear.Google Scholar
  17. [17]
    H. Rogers, Jr., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.MATHGoogle Scholar
  18. [18]
    R. I. Soare, The infinite injury priority method, J. Symbolic Logic 41 (1976), 513–530.MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    R. I. Soare, Fundamental methods for constructing recursively enumerable degrees, in Recursion Theory: Its Generalisations and Applications, Ed. by F. R. Drake and S. S. Wainer, Cambridge University Press, Cambridge (1980).Google Scholar
  20. [20]
    R. I. Soare, Recursively enumerable sets and degrees: the study of computable functions and computably generated sets, Springer Verlag, Berlin, Heidelberg, New York, to appear.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Carl G. JockuschJr.
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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