Tbilisi Mathematical Journal

The first almost free Whitehead group

Saharon Shelah

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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.


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.

Article information

Tbilisi Math. J., Volume 4 (2011), 17-28.

Received: 15 August 2007
Revised: 10 June 2011
Accepted: 12 September 2011
First available in Project Euclid: 12 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E75: Applications of set theory
Secondary: 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] 20K20: Torsion-free groups, infinite rank

Abelian group Whitehead group almost free stationary sets $\lambda$-sets


Shelah, Saharon. The first almost free Whitehead group. Tbilisi Math. J. 4 (2011), 17--28. https://projecteuclid.org/euclid.tbilisi/1528768865

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