A {\omega}-REA Set Forming A Minimal Pair With 0'
Logic
2011-01-04 v2
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 {\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".
Cite
@article{arxiv.1012.0950,
title = {A {\omega}-REA Set Forming A Minimal Pair With 0'},
author = {Peter M. Gerdes},
journal= {arXiv preprint arXiv:1012.0950},
year = {2011}
}