## On the existence of $\kappa$-free abelian groups

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- by Paul C. Eklof
- Proc. Amer. Math. Soc.
**47**(1975), 65-72 - DOI: https://doi.org/10.1090/S0002-9939-1975-0379694-0
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## Abstract:

It is proved that if ${\aleph _\alpha }$ is a regular cardinal such that there is an ${\aleph _\alpha }$-free abelian group which is not ${\aleph _{\alpha + 1}}$-free, then for every positive integer $n$ there is an ${\aleph _{\alpha + n}}$-free abelian group which is not ${\aleph _{\alpha + n + 1}}$-free. A corollary is that for each positive integer $n$ there is a group of cardinality ${\aleph _n}$ which is ${\aleph _n}$-free but not free. Some results on $\kappa$-free abelian groups which involve notions from logic are also proved.## References

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## Bibliographic Information

- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**47**(1975), 65-72 - MSC: Primary 02K20; Secondary 20K35
- DOI: https://doi.org/10.1090/S0002-9939-1975-0379694-0
- MathSciNet review: 0379694