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Interpreting true arithmetic in degree structures

A survey
  • André Nies
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 713)

Abstract

A survey of the techniques which lead to an interpretation of true arithmetic in the theories of the recursively enumerable many-one, truth-table and Turing degrees is given.

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References

  1. [Ambos-Spies, Nies, Shore92]
    K. Ambos-Spies, A. Nies, R. Shore. The theory of the r.e. weak truth-table degrees is undecidable. J. Symb. Logic, vol. 57, no. 3, Sept 1992, 864–874.Google Scholar
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    A. Nies. Definability and Undecidability in Recursion Theoretic Semilattices. Ph.D. thesis, Universität Heidelberg, 1992.Google Scholar
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    A. Nies, R. Shore. Interpreting arithmetic in the theory of the r.e. truth table degrees. Submitted.Google Scholar
  5. [Nies.Shore ta2]
    A. Nies, R. Shore. Interpreting true arithmetic in the theory of the tt-and wtt-degrees below Ø'. In preparation.Google Scholar
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    The theory of the degrees below Ø'. J. London Math. Soc (2), 24 (1981), 1–14.Google Scholar
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    T. Slaman, J. Shinoda. On the theory of the PTIME degrees of the recursive sets (abstract). Structure in Compl. Theory 4th conference, IEEE Comput. SocPress, 1989.Google Scholar
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    T. Slaman, W. Woodin. Definability in degree structures.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • André Nies
    • 1
  1. 1.Universität HeidelbergDeutschland

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