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
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.
A. Nies. Definability and Undecidability in Recursion Theoretic Semilattices. Ph.D. thesis, Universität Heidelberg, 1992.
A. Nies. The last question on recursively enumerable many-one degrees. Submitted.
A. Nies, R. Shore. Interpreting arithmetic in the theory of the r.e. truth table degrees. Submitted.
A. Nies, R. Shore. Interpreting true arithmetic in the theory of the tt-and wtt-degrees below Ø'. In preparation.
The theory of the degrees below Ø'. J. London Math. Soc (2), 24 (1981), 1–14.
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.
T. Slaman, W. Woodin. Definability in degree structures.
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© 1993 Springer-Verlag Berlin Heidelberg
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Nies, A. (1993). Interpreting true arithmetic in degree structures. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022574
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DOI: https://doi.org/10.1007/BFb0022574
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