Open Access
Translator Disclaimer
2011 The first almost free Whitehead group
Saharon Shelah
Author Affiliations +
Tbilisi Math. J. 4: 17-28 (2011). DOI: 10.32513/tbilisi/1528768865

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

Download Citation

Saharon Shelah. "The first almost free Whitehead group." Tbilisi Math. J. 4 17 - 28, 2011. https://doi.org/10.32513/tbilisi/1528768865

Information

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

zbMATH: 1278.03085
MathSciNet: MR2886755
Digital Object Identifier: 10.32513/tbilisi/1528768865

Subjects:
Primary: 03E75
Secondary: 03C60, 20K20

Rights: Copyright © 2011 Tbilisi Centre for Mathematical Sciences

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.4 • 2011
Back to Top