Abstract
We show that if $$2^{\aleph _0 } $$ Cohen reals are added to the universe, then for every reduced non-free torsion-free abelian groupA of cardinality less than the continuum, there is a primep so that Ext p (A,ℤ)≠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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