On the distribution of Lachlan nonsplitting bases

S. Barry Cooper, Angsheng Li, Xiaoding Yi
2002 Archive for Mathematical Logic  
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 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-Low 2 c.e. degree which bounds no Lachlan nonsplitting base.
doi:10.1007/s001530100095 fatcat:b5sa6jqm7zgxvil6v56uq7x3gu