Infima of d.r.e. degrees (Q2655142)

The authors obtain the following result: Given c.e. degrees \({\mathbf u}<{\mathbf v}\), there are d.c.e. degrees \({\mathbf a},{\mathbf b}_1,{\mathbf b}_2\) and a 3-c.e. degree \({\mathbf x}\) between \({\mathbf u}\) and \({\mathbf v}\) such that \({\mathbf a}<{\mathbf x}<{\mathbf b}_1,{\mathbf b}_2\) and \({\mathbf b}_1\) and \({\mathbf b}_2\) have infimum \({\mathbf a}\) in the d.c.e. degrees. This result extends \textit{D. Kaddah}'s result [Ann. Pure Appl. Logic 62, No. 3, 207--263 (1993; Zbl 0784.03023)] and implies that the isolated \(3\)-c.e. degrees are dense in the c.e. degrees, which was first proved by LaForte.