A minimal pair joining to a plus cupping Turing degree

✍ Scribed by Dengfeng Li; Angsheng Li

• Book ID: 102483021
• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 195 KB
• Volume: 49
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200310060

✦ Synopsis

Abstract

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)