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Published online by Cambridge University Press: 06 April 2016
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.