A minimal pair joining to a plus cupping Turing degree

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Mathematical Logic Quarterly 49 (6):553-566 (2003)
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Abstract

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

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10.1002/malq.200310060

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Citations of this work

On the definable ideal generated by the plus cupping c.e. degrees.Wei Wang & Decheng Ding - 2007 - Archive for Mathematical Logic 46 (3-4):321-346.

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References found in this work

A minimal pair of recursively enumerable degrees.C. E. M. Yates - 1966 - Journal of Symbolic Logic 31 (2):159-168.
Bounding minimal pairs.A. H. Lachlan - 1979 - Journal of Symbolic Logic 44 (4):626-642.
Recursively enumerable generic sets.Wolfgang Maass - 1982 - Journal of Symbolic Logic 47 (4):809-823.
Highness and bounding minimal pairs.Rodney G. Downey, Steffen Lempp & Richard A. Shore - 1993 - Mathematical Logic Quarterly 39 (1):475-491.

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