Abstract
We study prefix-free presentations of computably enumerable reals. In [2], Calude et. al. proved that a real α is c.e. if and only if there is an infinite, computably enumerable prefix-free set V such that α = Σσ∈V 2-|σ|. Following Downey and LaForte [5], we call V a prefixfree presentation of α. Each computably enumerable real has a computable presentation. Say that a c.e. real α is simple if each presentation of α is computable. Downey and LaForte [5] proved that simple reals locate on every jump class. In this paper, we prove that there is a noncomputable c.e. degree bounding no noncomputable simple reals. Thus, simple reals are not dense in the structure of computably enumerable degrees.
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