Is there an r.e. set $A$ such that 0’ is cuppable relative to $A$? What about cappable?
I’m pretty sure I’ve seen results on this and I’d hazard a guess they might even be in Odifreddi but it’s really hard to search for since 0’ turns up lots of false positives as do cupping and capping plus you have to decide to search for capping, cappable or minimal pair. If this has been asked here before I apologize but same problem.