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A minimal pair joining to a plus cupping Turing degree
Author(s) -
Li Dengfeng,
Li Angsheng
Publication year - 2003
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310060
Subject(s) - degree (music) , mathematics , combinatorics , turing , discrete mathematics , computer science , physics , acoustics , programming language
A computably enumerable (c.e.) 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 . (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)