Coding true arithmetic in the Medvedev and Muchnik degrees

@article{Shafer2011CodingTA,
  title={Coding true arithmetic in the Medvedev and Muchnik degrees},
  author={Paul Shafer},
  journal={J. Symb. Log.},
  year={2011},
  volume={76},
  pages={267-288}
}
We prove that the first-order theory of the Medvedev degrees, the first-order theory of the Muchnik degrees, and the third-order theory of true arithmetic are pairwise recursively isomorphic (obtained independently by Lewis, Nies, and Sorbi [7]). We then restrict our attention to the degrees of closed sets and prove that the following theories are pairwise recursively isomorphic: the first-order theory of the closed Medvedev degrees, the first-order theory of the compact Medvedev degrees, the… CONTINUE READING

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