A minimal pair joining to a plus cupping Turing degree

摘要

A computably enumerable (c. e.) degree α is called nonbounding, if it bounds no minimal pair, and plus cupping, if every nonzero c.e. degree x below α is cuppable. Let NB and PC be the sets of all nonbounding and plus cupping ce. degrees, respectively. Both NB and PC are well understood, but it has not been possible so far to distinguish between the two classes. In present paper, we investigate the relationship between the classes NB and PC, and show that there exists a minimal pair which joint to a plus cupping degree, so that PC is contained in NB. This gives a first known difference between NB and PC.