A minimal pair joining to a plus cupping Turing degree

  • Dengfeng Li*
  • , Angsheng Li
  • *Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)553-566
Number of pages14
JournalMathematical Logic Quarterly
Volume49
Issue number6
DOIs
StatePublished - 2003
Externally publishedYes

Keywords

  • Computably enumerable Turing degree
  • Minimal pair
  • Nounbounding degree
  • Plus cupping degree

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