A ω-REA Set Forming A Minimal Pair With 0'

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".