New Degree Spectra of Abelian Groups

Abstract

We show that for every computable ordinal of the form $\beta =\delta +2n+1>1$, where $\delta$ is zero or a limit ordinal and $n\in \omega$, there exists a torsion-free abelian group having an $X$-computable copy if and only if $X$ is nonlow${}_{\beta }$.