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Jump degrees of torsion-free abelian groups
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.Other Versions
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Citations of this work
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.
New Degree Spectra of Abelian Groups.Alexander G. Melnikov - 2017 - Notre Dame Journal of Formal Logic 58 (4):507-525.
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 orderings not isomorphic to recursive linear orderings.Carl G. Jockusch & Robert I. Soare - 1991 - Annals of Pure and Applied Logic 52 (1-2):39-64.
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