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# 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} }

- Published 2011 in J. Symb. Log.

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