# Sh:519

• Göbel, R., & Shelah, S. (1995). On the existence of rigid \aleph_1-free abelian groups of cardinality \aleph_1. In Abelian groups and modules (Padova, 1994), Vol. 343, Kluwer Acad. Publ., Dordrecht, pp. 227–237.
• Abstract:
An abelian group is said to be \aleph_1–free if all its countable subgroups are free. Our main result is:

If R is a ring with R^+ free and |R|<\lambda\leq 2^{\aleph_0}, then there exists an \aleph_1–free abelian group G of cardinality \lambda with {\rm End} G = R.

A corollary to this theorem is:

Indecomposable \aleph_1–free abelian groups of cardinality \aleph_1 do exist.

• Version 2001-02-12_11 (10p) published version (11p)
Bib entry
@incollection{Sh:519,
author = {G{\"o}bel, R{\"u}diger and Shelah, Saharon},
title = {{On the existence of rigid $\aleph_1$-free abelian groups of cardinality $\aleph_1$}},
booktitle = {{Abelian groups and modules (Padova, 1994)}},
series = {Math. Appl.},
volume = {343},
year = {1995},
pages = {227--237},
publisher = {Kluwer Acad. Publ., Dordrecht},
mrnumber = {1378201},
mrclass = {20K20 (03C60 20K40)},
note = {\href{https://arxiv.org/abs/math/0104194}{arXiv: math/0104194}},
arxiv_number = {math/0104194}
}