## Tbilisi Mathematical Journal

### The first almost free Whitehead group

Saharon Shelah

#### 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.

#### Note

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

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

Dates
Revised: 10 June 2011
Accepted: 12 September 2011
First available in Project Euclid: 12 June 2018

https://projecteuclid.org/euclid.tbilisi/1528768865

Mathematical Reviews number (MathSciNet)
MR2886755

Zentralblatt MATH identifier
1278.03085

#### Citation

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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