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Jump degrees of torsion-free abelian groups. (English) Zbl 1273.03142
Summary: We show, for each computable ordinal \(\alpha\) and degree \(\mathbf{a} > \mathbf{0}^{(\alpha)}\), the existence of a torsion-free abelian group with proper \(\alpha^{\mathrm{th}}\) jump degree \(\mathbf{a}\).

MSC:
03D45 Theory of numerations, effectively presented structures
20K15 Torsion-free groups, finite rank
20K20 Torsion-free groups, infinite rank
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