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arXiv · 1504.02805

DNR and incomparable Turing degrees

Mingzhong Cai·Noam Greenberg·Michael McInerney
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Abstract

We construct an increasing $\omega$-sequence $(a_n)$ of Turing degrees which forms an initial segment of the Turing degrees, and such that each~$a_{n+1}$ is diagonally noncomputable relative to $a_n$. It follows that the~$\mathsf{DNR}$ principle of reverse mathematics does not imply the existence of Turing incomparable degrees.

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Mingzhong Cai, Noam Greenberg, Michael McInerney. 2015-04-10. DNR and incomparable Turing degrees. https://arxiv.org/abs/1504.02805

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