A {\omega}-REA Set Forming A Minimal Pair With 0'
PM Gerdes�- arXiv preprint arXiv:1012.0950, 2010 - arxiv.org
arXiv preprint arXiv:1012.0950, 2010•arxiv.org
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".
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".
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".
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