Relatively computably enumerable reals
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 Pi01 class contains a member which is not relatively c.e. and that every 1-generic real is relatively simple and above.
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