## The structure of $\omega _{1}$-separable groups

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- by Paul C. Eklof
- Trans. Amer. Math. Soc.
**279**(1983), 497-523 - DOI: https://doi.org/10.1090/S0002-9947-1983-0709565-8
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## Abstract:

A classification theorem is proved for ${\omega _1}$-separable ${\omega _1}$-free abelian groups of cardinality ${\omega _1}$ assuming Martin’s Axiom $(\text {MA})$ and ${2^{\aleph _0}} > {\aleph _1}$. As a consequence, several structural results about direct sum decompositions of ${\omega _1}$-separable groups are proved. These results are proved independent of $\text {ZFC}$, and, in addition, another structural property is proved undecidable in ${\text {ZFC}} + {\text {MA}} + {2^{\aleph _0}} > {\aleph _1}$. The problem of classifying these groups in a model of ${2^{\aleph _0}} = {\aleph _1}$ is also investigated.## References

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## Bibliographic Information

- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**279**(1983), 497-523 - MSC: Primary 03E35; Secondary 03E50, 20A15, 20K20
- DOI: https://doi.org/10.1090/S0002-9947-1983-0709565-8
- MathSciNet review: 709565