2000/11/22 by Rüdiger Göbel, Saharon Shelah
Mathematics · #math.GR #math.LO
published as Proceedings of the Conference on Abelian Groups in Colorado Springs (1995), volume 182 of Lecture Notes in Pure and Applied Math., pp 253-271, Marcel Dekker 1996
arxiv created 2000/11/22 · arxiv updated 2009/11/30
We begin with the existence of groups with trivial duals for cardinals alephn (n in omega). Then we derive results about strongly alephn-free abelian groups of cardinality alephn (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 >alephomega. 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 alephomega. Recall that alephomega is the first singular cardinal and such groups of cardinality alephomega do not exist by the well-known Singular Compactness Theorem (see [Sh:52]).