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