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Degrees of orders on torsion-free abelian groups. (English) Zbl 1323.03058
Summary: We show that if \(H\) is an effectively completely decomposable computable torsion-free abelian group, then there is a computable copy \(G\) of \(H\) such that \(G\) has computable orders but not orders of every (Turing) degree.

MSC:
03D45 Theory of numerations, effectively presented structures
03C57 Computable structure theory, computable model theory
03D28 Other Turing degree structures
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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