Splitting into degrees with low computational strength |
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Authors: | Rod Downey Keng Meng Ng |
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Institution: | 1. School of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington, New Zealand;2. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Republic of Singapore |
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Abstract: | 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 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. |
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Keywords: | 03D25 Degree splitting c e degrees Lowness Superlow Array computable |
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