## 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

### Keywords:

torsion-free abelian group; jump degree
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### References:

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