Abstract
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 ω-REA set can form a (non-trivial) minimal pair with 0". Shore has asked whether this can be improved to show that no ω-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 α-REA set can form a (non-trivial) minimal pair with 0".
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