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Relative enumerability and 1-genericity

Published online by Cambridge University Press:  12 March 2014

Wei Wang
Wei Wang*
Affiliation:
Institute of Logic and Cognition and Department of Philosophy, Sun Yat-Sen University, 135 Xingang Xi Road, Guangzhou 510275, Pr., China, E-mail: wwang.cn@gmail.com
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Abstract

A set of natural numbers B is computably enumerable in and strictly above (or c.e.a. for short) another set C if C <TB and B is computably enumerable in C. A Turing degree b is c.e.a. c if b and c respectively contain B and C as above. In this paper, it is shown that if b is c.e.a. c then b is c.e.a. some 1-generic g.

Keywords

Turing degreesrelative enumerability1-generic
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 3 , September 2011 , pp. 897 - 913
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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