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Published in:
2006 | OriginalPaper | Chapter
A Generic Set That Does Not Bound a Minimal Pair
Author : Mariya Ivanova Soskova
Published in: Theory and Applications of Models of Computation
Publisher: Springer Berlin Heidelberg
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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.