Relatively computably enumerable reals
Logic
2011-06-14 v2
Abstract
A real X is defined to be relatively c.e. if there is a real Y such that X is c.e.(Y) and Y does not compute X. A real X is relatively simple and above if there is a real Y <_T X such that X is c.e.(Y) and there is no infinite subset Z of the complement of X such that Z is c.e.(Y). We prove that every nonempty Pi^0_1 class contains a member which is not relatively c.e. and that every 1-generic real is relatively simple and above.
Keywords
Cite
@article{arxiv.0705.0776,
title = {Relatively computably enumerable reals},
author = {Bernard A. Anderson},
journal= {arXiv preprint arXiv:0705.0776},
year = {2011}
}