Maximal pairs of c.e. reals in the computably Lipschitz degrees

Computably Lipschitz reducibility (noted as ≤cl for short), was suggested as a measure of relative randomness. We say α≤clβ if α is Turing reducible to β with oracle use on x bounded by x+c. In this paper, we prove that for any non-computable real, there exists a c.e. real so that no c.e. real can cl-compute both of them. So every non-computable c.e. real is the half of a cl-maximal pair of c.e. reals.