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Computably Enumerable Sets in the Solovay and the Strong Weak Truth Table Degrees

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New Computational Paradigms (CiE 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3526))

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Abstract

The strong weak truth table reducibility was suggested by Downey, Hirschfeldt, and LaForte as a measure of relative randomness, alternative to the Solovay reducibility. It also occurs naturally in proofs in classical computability theory as well as in the recent work of Soare, Nabutovsky and Weinberger on applications of computability to differential geometry. Yu and Ding showed that the relevant degree structure restricted to the c.e. reals has no greatest element, and asked for maximal elements. We answer this question for the case of c.e. sets. Using a doubly non-uniform argument we show that there are no maximal elements in the sw degrees of the c.e. sets. We note that the same holds for the Solovay degrees of c.e. sets.

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References

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Leeds, Leeds, LS2 9JT, U.K

    George Barmpalias

Authors
  1. George Barmpalias
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Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.

    S. Barry Cooper

  2. Department Mathematik, Universität Hamburg, Bundesstrasse 55, 20146, Hamburg, Germany

    Benedikt Löwe

  3. Universiteit van Amsterdam,  

    Leen Torenvliet

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© 2005 Springer-Verlag Berlin Heidelberg

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Barmpalias, G. (2005). Computably Enumerable Sets in the Solovay and the Strong Weak Truth Table Degrees. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_2

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  • DOI: https://doi.org/10.1007/11494645_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26179-7

  • Online ISBN: 978-3-540-32266-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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