DNR and incomparable Turing degrees

الأصل · EN

We construct an increasing ω-sequence (aₙ) of Turing degrees which forms an initial segment of the Turing degrees, and such that each aₙ₊₁ is diagonally noncomputable relative to aₙ. It follows that the DNR principle of reverse mathematics does not imply the existence of Turing incomparable degrees.