Cupping and jump classes in the computably enumerable degrees

• Main Authors: Greenberg, Noam, Ng, Keng Meng, Wu, Guohua
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Array Computable; Computably Enumerable Degrees
• Online Access: https://hdl.handle.net/10356/154823
• Institution: Nanyang Technological University

We show that there is a cuppable c.e. degree, all of whose cupping partners are high. In particular, not all cuppable degrees are -cuppable, or indeed 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...