It is easy to see that no n-REA set can form a (non-trivial) minimal pair with 0' and only slightly more difficult to observe that no { \omega}-REA set can form a (non-trivial) minimal pair with 0". Shore has asked whether this can be improved to show that no { \omega}-REA set forms a (non-trivial) minimal pair with 0'. We show that no such improvement is possible by constructing a non-computable set C computable from 0" forming a minimal pair with 0'. We then show that no { \alpha}-REA set can form a (non-trivial) minimal pair with 0".
Categories: math.LO