New Degree Spectra of Abelian Groups

Notre Dame Journal of Formal Logic 58 (4):507-525 (2017)
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Abstract

We show that for every computable ordinal of the form β=δ+2n+1>1, where δ is zero or a limit ordinal and n∈ω, there exists a torsion-free abelian group having an X-computable copy if and only if X is nonlowβ.

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10.1215/00294527-2017-0006

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Alexander Melnikov
National Research University Higher School of Economics

Citations of this work

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

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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