A note on the Turing degree of divergence bounded computable real numbers (2004)
by
Xizhong Zheng
,
Robert Rettinger
| Venue: | CCA 2004, August 16-20, Lutherstadt |
| Citations: | 2 - 1 self |
BibTeX
@INPROCEEDINGS{Zheng04anote,
author = {Xizhong Zheng and Robert Rettinger},
title = {A note on the Turing degree of divergence bounded computable real numbers},
booktitle = { CCA 2004, August 16-20, Lutherstadt},
year = {2004},
publisher = {}
}
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Abstract
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 [2] and show that there exists a ∆0 2-Turing degree which contains no divergence bounded computable real numbers. This extends the result of [2] that not every ∆0 2-Turing degree contains a d-c.e. real.
