Totally < ωω Computably Enumerable and m-topped Degrees

  • Rod Downey
  • Noam Greenberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)


In this paper we will discuss recent work of the authors (Downey, Greenberg and Weber [8] and Downey and Greenberg [6, 7]) devoted to understanding some new naturally definable degree classes which capture the dynamics of various natural constructions arising from disparate areas of classical computability theory.

It is quite rare in computability theory to find a single class of degrees which capture precisely the underlying dynamics of a wide class of apparently similar constructions, demonstrating that they all give the same class of degrees. A good example of this phenomenon is work pioneered by Martin [22] who identified the high c.e. degrees as the ones arising from dense simple, maximal, hh-simple and other similar kinds of c.e. sets constructions. Another example would be the example of the promptly simple degrees by Ambos-Spies, Jockusch, Shore and Soare [2]. Another more recent example of current great interest is the class of K-trivial reals of Downey, Hirscheldt, Nies and Stephan [5], and Nies [23, 24].


Computable Function Computability Theory Computable Approximation Accessible Node Recursion Theory 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rod Downey
    • 1
  • Noam Greenberg
    • 1
  1. 1.School of Mathematics, Statistics, and Computer ScienceVictoria UniversityWellingtonNew Zealand

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