Every coseparable group may be free
Logic
2016-09-06 v1 Rings and Algebras
Abstract
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.
Cite
@article{arxiv.math/9305205,
title = {Every coseparable group may be free},
author = {Alan H. Mekler and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9305205},
year = {2016}
}