On the distribution of Lachlan nonsplitting bases (Q1407550)

We say that a computably enumerable (c.e.) degree \(b\) is a Lachlan nonsplitting base if there is a c.e. degree \(a\) such that \(a> b\) and for any c.e. degrees \(w\), \(v\), if \(b\leq w\), \(v< a\), then \(w\vee v< a\). In this paper the authors investigate the relationship between bounding and nonbounding of Lachlan nonsplitting bases and the high/low hierarchy. The main result of this paper is the following theorem: There exists a non-Low\(_2\) c.e. degree which bounds no Lachlan nonsplitting base.