Sh:579

• Göbel, R., & Shelah, S. (1996). GCH implies existence of many rigid almost free abelian groups. In Abelian groups and modules (Colorado Springs, CO, 1995), Vol. 182, Dekker, New York, pp. 253–271. arXiv: math/0011185 MR: 1415638
• Abstract:
  We begin with the existence of groups with trivial duals for cardinals \aleph_n (n\in \omega). Then we derive results about strongly \aleph_n-free abelian groups of cardinality \aleph_n (n\in\omega) with prescribed free, countable endomorphism ring. Finally we use combinatorial results of [Sh:108], [Sh:141] to give similar answers for cardinals >\aleph_\omega. As in Magidor and Shelah [MgSh:204], a paper concerned with the existence of \kappa-free, non-free abelian groups of cardinality \kappa, the induction argument breaks down at \aleph_\omega. Recall that \aleph_\omega is the first singular cardinal and such groups of cardinality \aleph_\omega do not exist by the well-known Singular Compactness Theorem (see [Sh:52]).
• Version 2000-10-31_10 (22p) published version (19p)

@incollection{Sh:579,
 author = {G{\"o}bel, R{\"u}diger and Shelah, Saharon},
 title = {{GCH implies existence of many rigid almost free abelian groups}},
 booktitle = {{Abelian groups and modules (Colorado Springs, CO, 1995)}},
 series = {Lecture Notes in Pure and Appl. Math.},
 volume = {182},
 year = {1996},
 pages = {253--271},
 publisher = {Dekker, New York},
 mrnumber = {1415638},
 mrclass = {20K20 (03E75 04A30)},
 note = {\href{https://arxiv.org/abs/math/0011185}{arXiv: math/0011185}},
 arxiv_number = {math/0011185}
}