On the existence of rigid aleph1-free abelian groups of cardinality aleph1
Rüdiger Göbel, Saharon Shelah
Abstract
An abelian group is said to be aleph1-free if all its countable subgroups are free. Our main result is: If R is a ring with R+ free and |R|<lambda <= 2aleph0, then there exists an aleph1-free abelian group G of cardinality lambda with End(G)=R . A corollary to this theorem is: Indecomposable aleph1-free abelian groups of cardinality aleph1 do exist.
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