A generic set that does not bound a minimal pair

  • Authors:

  • Mariya Ivanova Soskova

  • Affiliations:

  • University of Leeds

  • Venue:
  • TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
  • Year:
  • 2006

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Abstract

The structure of the semi lattice of enumeration degrees has been investigated from many aspects. One aspect is the bounding and nonbounding properties of generic degrees. Copestake proved that every 2-generic enumeration degree bounds a minimal pair and conjectured that there exists a 1-generic set that does not bound a minimal pair. In this paper we verify this longstanding conjecture by constructing such a set using an infinite injury priority argument. The construction is explained in detail. It makes use of a priority tree of strategies.