Bounding and nonbounding minimal pairs in the enumeration degrees. (English) Zbl 1093.03029
In this very interesting paper it is proved that: 1) Every nonzero \(\Delta^0_2\) e-degree bounds a minimal pair. Every nonzero \(\Delta^0_2\) s-degree bounds a minimal pair of s-degrees. 2) There exists a nonzero \(\Sigma^0_2\) e-degree which bounds no minimal pairs. There exists a nonzero \(\Sigma^0_2\) s-degree that does not bound any minimal pair of s-degrees.
Reviewer: Roland Sh. Omanadze (Tbilisi)
MSC:
03D30 | Other degrees and reducibilities in computability and recursion theory |
03D25 | Recursively (computably) enumerable sets and degrees |
References:
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