A Note On the Turing Degrees of Divergence Bounded Computable Reals | Zendy

Xizhong Zheng | Zendy; Robert Rettinger | Zendy

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A Note On the Turing Degrees of Divergence Bounded Computable Reals

Author(s) -

Xizhong Zheng,

Robert Rettinger

Publication year - 2005

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2004.06.047

Subject(s) - turing , degree (music) , computable number , bounded function , mathematics , discrete mathematics , turing machine , divergence (linguistics) , combinatorics , computable function , computer science , algorithm , computable analysis , computation , mathematical analysis , linguistics , physics , philosophy , acoustics , programming language

The Turing degree of a real number is defined as the Turing degree of its binary expansion. In this note we apply the double witnesses technique recently developed by Downey, Wu and Zheng [R. Downey, G. Wu, and X. Zheng. Degrees of d.c.e. reals. Mathematical Logic Quartely, 2004. (to appear)] and show that there exists a Δ20-Turing degree which contains no divergence bounded computable real numbers. This extends the result of [R. Downey, G. Wu, and X. Zheng. Degrees of d.c.e. reals. Mathematical Logic Quartely, 2004. (to appear)] that not every Δ20-Turing degree contains a d-c.e. real

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