Jump degrees of torsion-free abelian groups

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

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10.2178/jsl.7704020

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Citations of this work

Computable Abelian groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.
New Degree Spectra of Abelian Groups.Alexander G. Melnikov - 2017 - Notre Dame Journal of Formal Logic 58 (4):507-525.
Torsion-free abelian groups with optimal Scott families.Alexander G. Melnikov - 2018 - Journal of Mathematical Logic 18 (1):1850002.

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References found in this work

Computable structures and the hyperarithmetical hierarchy.C. J. Ash - 2000 - New York: Elsevier. Edited by J. Knight.
Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
Degrees coded in jumps of orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.
Degrees of structures.Linda Jean Richter - 1981 - Journal of Symbolic Logic 46 (4):723-731.

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