Relatively computably enumerable reals

Details Relatively computably enumerable reals Relatively computably enumerable reals

2007-05-06

arxiv.org/abs/0705.0776v2

Archive for Mathematical Logic, Volume 50, Number 3-4, May 2011, pp. 361-365

Mathematics

Logic

5 pages. Significant changes from earlier version

Scientific paper

10.1007/s00153-010-0219-2

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.

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