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Computability and Complexity pp 563–598Cite as

On the Strongly Bounded Turing Degrees of the Computably Enumerable Sets

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10010))

Abstract

We introduce and discuss some techniques designed for the study of the strongly bounded Turing degrees of the computably enumerable sets, i.e., of the computable Lipschitz degrees and of the identity bounded Turing degrees of c.e. sets. In particular we introduce some tools which allow the transfer of certain facts on the weak truth-table degrees to these degree structures. Using this approach we show that the first order theories of the partial orderings \((\mathrm {R}_\mathrm {cl},\le )\) and \((\mathrm {R}_\mathrm {ibT},\le )\) of the c.e. \(\mathrm {cl}\)- and \(\mathrm {ibT}\)-degrees are not \(\aleph _0\)-categorical and undecidable. Moreover, various other results on the structure of the partial orderings \((\mathrm {R}_\mathrm {cl},\le )\) and \((\mathrm {R}_\mathrm {ibT},\le )\) are obtained along these lines.

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Authors and Affiliations

  1. Institut für Informatik, Heidelberg University, INF 205, 69120, Heidelberg, Germany

    Klaus Ambos-Spies

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  1. Klaus Ambos-Spies
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Correspondence to Klaus Ambos-Spies .

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Editors and Affiliations

  1. Victoria University of Wellington, Wellington, New Zealand

    Adam Day

  2. University of Bergen, Bergen, Norway

    Michael Fellows

  3. Victoria University of Wellington, Wellington, New Zealand

    Noam Greenberg

  4. University of Auckland, Auckland, New Zealand

    Bakhadyr Khoussainov

  5. Massey University, Auckland, New Zealand

    Alexander Melnikov

  6. University of Bergen, Bergen, Norway

    Frances Rosamond

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Ambos-Spies, K. (2017). On the Strongly Bounded Turing Degrees of the Computably Enumerable Sets. In: Day, A., Fellows, M., Greenberg, N., Khoussainov, B., Melnikov, A., Rosamond, F. (eds) Computability and Complexity. Lecture Notes in Computer Science(), vol 10010. Springer, Cham. https://doi.org/10.1007/978-3-319-50062-1_34

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  • DOI: https://doi.org/10.1007/978-3-319-50062-1_34

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  • Online ISBN: 978-3-319-50062-1

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