## Notre Dame Journal of Formal Logic

### New Degree Spectra of Abelian Groups

Alexander G. Melnikov

#### Abstract

We show that for every computable ordinal of the form $\beta=\delta+2n+1\gt 1$, where $\delta$ is zero or a limit ordinal and $n\in\omega$, there exists a torsion-free abelian group having an $X$-computable copy if and only if $X$ is nonlow$_{\beta}$.

#### Article information

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

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

https://projecteuclid.org/euclid.ndjfl/1494640857

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

Mathematical Reviews number (MathSciNet)
MR3707649

Zentralblatt MATH identifier
06803185

#### 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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