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Every coseparable group may be free

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.

preprint1993arXivOpen access
Alan H. MeklerSaharon Shelah
math.LOmath.RA
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Alan H. MeklerSaharon Shelah

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