Article contents
DNR AND INCOMPARABLE TURING DEGREES
Published online by Cambridge University Press: 06 April 2016
Abstract
We construct an increasing ${\it\omega}$-sequence $\langle \boldsymbol{a}_{n}\rangle$ of Turing degrees which forms an initial segment of the Turing degrees, and such that each $\boldsymbol{a}_{n+1}$ is diagonally nonrecursive relative to $\boldsymbol{a}_{n}$. It follows that the DNR principle of reverse mathematics does not imply the existence of Turing incomparable degrees.
MSC classification
- Type
- Research Article
- Information
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © The Author(s) 2016
References
- 1
- Cited by