Spectra of atomic theories

Abstract

For a countable structure $\mathcal{B}$, the spectrum is the set of Turing degrees of isomorphic copies of $\mathcal{B}$. For a complete elementary first order theory $T$, the spectrum is the set of Turing degrees of models of $T$. We answer a question from [1] by showing that there is an atomic theory $T$ whose spectrum does not match the spectrum of any structure.