Journal of Symbolic Logic 77 (4):1067-1100 (2012)

Abstract
We show, for each computable ordinal α and degree $\alpha > {0^{\left( \alpha \right)}}$, the existence of a torsion-free abelian group with proper α th jump degree α
Keywords torsion-free abelian group   jump degree
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DOI 10.2178/jsl.7704020
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References found in this work BETA

Countable Algebra and Set Existence Axioms.Harvey M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.
Degrees Coded in Jumps of Orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.
Reverse Mathematics and Fully Ordered Groups.Reed Solomon - 1998 - Notre Dame Journal of Formal Logic 39 (2):157-189.

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Citations of this work BETA

Computable Abelian Groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.
Torsion-Free Abelian Groups with Optimal Scott Families.Alexander G. Melnikov - 2018 - Journal of Mathematical Logic 18 (1):1850002.

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