### Every coseparable group may be free

by Mekler and Shelah. [MkSh:418]

Israel J Math, 1993

We show that if 2^{aleph_0} Cohen reals are added to
the universe, then for every reduced non-free torsion-free
abelian group A of cardinality less than the continuum, there
is a prime p so that Ext_p(A, Z) not= 0 . In
particular if it is consistent that there is a supercompact
cardinal, then it is consistent (even with weak CH) that every
coseparable group is free. The use of some large cardinal
hypothesis is needed.

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