Rocky Mountain Journal of Mathematics

The classification of infinite abelian groups with partial decomposition bases in $L_\infty \omega $

Carol Jacoby and Peter Loth

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Abstract

We consider the class of abelian groups with partial decomposition bases, which includes groups classified by Ulm, Warfield, Stanton and others. We define an invariant and classify these groups in the language $L_{\infty \omega }$, or equivalently, up to partial isomorphism. This generalizes a result of Barwise and Eklof and builds on Jacoby's classification of local groups with partial decomposition bases in $L_{\infty \omega }$.

Article information

Source
Rocky Mountain J. Math. Volume 47, Number 2 (2017), 463-477.

Dates
First available in Project Euclid: 18 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1492502546

Digital Object Identifier
doi:10.1216/RMJ-2017-47-2-463

Subjects
Primary: 03C52: Properties of classes of models 13C05: Structure, classification theorems 20K21: Mixed groups
Secondary: 03E10: Ordinal and cardinal numbers 20K25: Direct sums, direct products, etc. 20K35: Extensions

Keywords
Partial decomposition basis partial isomorphism infinitary equivalence Ulm-Kaplansky invariants Warfield invariants

Citation

Jacoby, Carol; Loth, Peter. The classification of infinite abelian groups with partial decomposition bases in $L_\infty \omega $. Rocky Mountain J. Math. 47 (2017), no. 2, 463--477. doi:10.1216/RMJ-2017-47-2-463. https://projecteuclid.org/euclid.rmjm/1492502546.


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References

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