Every coseparable group may be free

Details Every coseparable group may be free Every coseparable group may be free

1993-05-15

arxiv.org/abs/math/9305205v1

Israel J. Math. 81 (1993), 161--178

Mathematics

Logic

Scientific paper

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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