Splitting into degrees with low computational strength

We investigate the extent to which a c.e. degree can be split into two smaller c.e. degrees which are computationally weak. In contrast to a result of Bickford and Mills that 0′ can be split into two superlow c.e. degrees, we construct a SJT-hard c.e. degree which is not the join of two superlow c.e...

全面介紹

Saved in:
書目詳細資料
Main Authors: Downey, Rod, Ng, Keng Meng
其他作者: School of Physical and Mathematical Sciences
格式: Article
語言:English
出版: 2020
主題:
在線閱讀:https://hdl.handle.net/10356/142074
標簽: 添加標簽
沒有標簽, 成為第一個標記此記錄!
機構: Nanyang Technological University
語言: English
實物特徵
總結:We investigate the extent to which a c.e. degree can be split into two smaller c.e. degrees which are computationally weak. In contrast to a result of Bickford and Mills that 0′ can be split into two superlow c.e. degrees, we construct a SJT-hard c.e. degree which is not the join of two superlow c.e. degrees. We also prove that every high c.e. degree is the join of two array computable c.e. degrees, and that not every high2 c.e. degree can be split in this way. Finally we extend a result of Downey, Jockusch and Stob by showing that no totally ω-c.a. wtt-degree can be cupped to the complete wtt-degree.