Lattice embedding into d-r. e. degrees preserving 0 and 1 (Q2784779)

The following theorems are established: There are an r.e. degree \({\mathbf a}\) and a d.r.e. degree \({\mathbf b}\) such that \(\mathbf{0}<{\mathbf a}<\text\textbf{0}'\), \(\mathbf{0}<{\mathbf b}<\text\textbf{0}'\), \({\mathbf a}\cup{\mathbf b}=\mathbf{0}'\) and \({\mathbf a}\cap{\mathbf b}=\mathbf{0}\). There are an r.e. degree \({\mathbf a}>\mathbf{0}\) and d.r.e. degrees \({\mathbf b}\), \({\mathbf c}> \mathbf{0}\) such that \({\mathbf a}\cup {\mathbf b}={\mathbf b}\cup{\mathbf c}=\mathbf{0}'\) and \({\mathbf a}\cap{\mathbf b}={\mathbf b}\cap{\mathbf c}={\mathbf c}\cap{\mathbf a}=\mathbf{0}\). There are r.e. degrees \({\mathbf a}\), \({\mathbf b}>\mathbf{0}\) and a d.r.e. degree \({\mathbf c}>\mathbf{0}\) such that \({\mathbf a}<{\mathbf b}\), \({ \mathbf a}\cup{\mathbf c}=\mathbf{0}'\) and \({\mathbf b}\cap{\mathbf c}=\mathbf{0}\).NEWLINENEWLINEFor the entire collection see [Zbl 0970.00012].