The \(\Delta_2^0\)-spectrum of a linear order
The spectrum \(\text{Spec}(S)\) of an algebraic structure \(S\) is the class of Turing degrees of presentations of \(S\). Slaman and independently Wehner constructed an example of a structure with \(\text{Spec}(S)= {\mathbf D}\setminus \{\mathbf{0}\}\) where \textbf{D} is the class of all Turing degrees. Answering a question of Downey, the author constructs an example of a linear order whose spectrum includes every non-computable \(\Delta_2^0\)-degree.
scientific article; zbMATH DE number 1658156