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DNR and incomparable Turing degrees
- Publication Year :
- 2015
-
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.
- Subjects :
- Mathematics - Logic
03D28, 03b30, 03f35
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1504.02805
- Document Type :
- Working Paper