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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
