Abstract
Assume $\mathsf{GCH}$ and that $\kappa$ is the first uncountable cardinal such that there is a non-free $\kappa$-free Abelian Whitehead group of cardinality $\kappa$. We prove that if all $\kappa$-free Abelian groups of cardinality $\kappa$ are Whitehead then $\kappa$ is necessarily an inaccessible cardinal.
Funding Statement
Research supported by German-Israeli Foundation for Scientific Research/Development Grant No. I-706-54.6/2001. Publication 914. I would like to thank Alice Leonhardt for her typing. We should like to thank the referees for many helpful comments, in particular for making the work more self-contained.
Citation
Saharon Shelah. "The first almost free Whitehead group." Tbilisi Math. J. 4 17 - 28, 2011. https://doi.org/10.32513/tbilisi/1528768865
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