CUPPING AND JUMP CLASSES IN THE COMPUTABLY ENUMERABLE DEGREES

We show that there is a cuppable c.e. degree, all of whose cupping partners are high. In particular, not all cuppable degrees are low₃-cuppable, or indeed low n cuppable for any n, refuting a conjecture by Li. On the other hand, we show that one cannot improve highness to superhighness. We also show...

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Bibliographic Details
Published in:The Journal of symbolic logic 2020-12, Vol.85 (4), p.1499-1545
Main Authors: GREENBERG, NOAM, NG, KENG MENG, WU, GUOHUA
Format: Article
Language:English
Subjects:
Approximation
Logic
Mathematics
Philosophy
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Summary:We show that there is a cuppable c.e. degree, all of whose cupping partners are high. In particular, not all cuppable degrees are low₃-cuppable, or indeed low n cuppable for any n, refuting a conjecture by Li. On the other hand, we show that one cannot improve highness to superhighness. We also show that the low₂-cuppable degrees coincide with the array computable-cuppable degrees, giving a full understanding of the latter class.
ISSN:0022-4812
1943-5886
DOI:10.1017/jsl.2020.36