On the distribution of Lachlan nonsplitting bases

@article{Cooper2002OnTD,
  title={On the distribution of Lachlan nonsplitting bases},
  author={S. Barry Cooper and Angsheng Li and Xiaoding Yi},
  journal={Archive for Mathematical Logic},
  year={2002},
  volume={41},
  pages={455-482}
}
Abstract. We say that a computably enumerable (c.e.) degree b is a Lachlan nonsplitting base(LNB), if there is a computably enumerable degree a such that a > b, and for any c.e. degrees w,v ≤ a, if a ≤ w or; v or; b then either a ≤ w or; b or a ≤ v or; b. In this paper we investigate the relationship between bounding and nonbounding of Lachlan nonsplitting bases and the high /low hierarchy. We prove that there is a non-Low2 c.e. degree which bounds no Lachlan nonsplitting base. 

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