Summary: A computable presentation of the linearly ordered set \((\omega,\le)\), where \(\omega\) is the set of natural numbers and \(\le\) is the natural order on \(\omega\), is any linearly ordered set \(\mathbf{L}=(\omega,\le_L)\) isomorphic to \((\omega,\le)\) such that \(\le_L\) is a computable relation. Let \(X\) be subset of \(\omega\) and \(X_L\) be the image of \(X\) in the linear order \(\mathbf{L}\) under the isomorphism between \((\omega,\le)\) and \(\mathbf{L}\). The degree spectrum of \(X\) is the set of all Turing degrees of \(X_L\) as one runs over all computable presentations of \((\omega,\le)\). In this paper we study the degree spectra of subsets of \(\omega\).
For the entire collection see [Zbl 1309.03002].