In this paper, we prove that if a c.e. Turing degree d is non-low2, then there are two left-c.e. reals β 0, β 1 in d, such that, if β 0 is wtt-reducible to a left-c.e. real α, then β 1 is not computable Lipschitz (cl-) reducible to α. As a corollary, d contains a left-c.e. real which is not cl-reducible to any complex (wtt-complete) left-c.e. real.
Acta Mathematica Sinica, English Series – Springer Journals
Published: Jun 25, 2017
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