DNR and Incomparable Turing Degrees

Document Type

Article

Publication Date

4-6-2016

Publication Title

Forum of Mathematics Sigma

Department

Department of Mathematics

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 nonrecursive relative to a(n). It follows that the DNR principle of reverse mathematics does not imply the existence of Turing incomparable degrees.

DOI

10.1017/fms.2016.3

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