The partial orderings of the computably enumerable ibT-degrees and cl-degrees are not elementarily equivalent

We show that, in the partial ordering (Rcl,⩽) of the computably enumerable (c.e.) computable Lipschitz (cl) degrees, there is a degree a>0 such that the class of the degrees which do not cup to a is not bounded by any degree less than a. Since Ambos-Spies (in press) [1] has shown that, in the partial ordering (RibT,⩽) of the c.e. identity-bounded Turing (ibT) degrees, for any degree a>0 the degrees which do not cup to a are bounded by the 1-shift a+1 of a where a+1