Notre Dame Journal of Formal Logic

New Degree Spectra of Abelian Groups

Alexander G. Melnikov

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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 nω, there exists a torsion-free abelian group having an X-computable copy if and only if X is nonlowβ.

Article information

Source
Notre Dame J. Formal Logic, Volume 58, Number 4 (2017), 507-525.

Dates
Received: 9 December 2013
Accepted: 23 December 2014
First available in Project Euclid: 13 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1494640857

Digital Object Identifier
doi:10.1215/00294527-2017-0006

Mathematical Reviews number (MathSciNet)
MR3707649

Zentralblatt MATH identifier
06803185

Subjects
Primary: 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
Secondary: 03C57: Effective and recursion-theoretic model theory [See also 03D45] 20K20: Torsion-free groups, infinite rank

Keywords
abelian groups degree spectra computable structures

Citation

Melnikov, Alexander G. New Degree Spectra of Abelian Groups. Notre Dame J. Formal Logic 58 (2017), no. 4, 507--525. doi:10.1215/00294527-2017-0006. https://projecteuclid.org/euclid.ndjfl/1494640857


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