# Sh:418

- Mekler, A. H., & Shelah, S. (1993).
*Every coseparable group may be free*. Israel J. Math.,**81**(1-2), 161–178. arXiv: math/9305205 DOI: 10.1007/BF02761303 MR: 1231184 -
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 {\rm Ext}_p(A, {\mathbb Z}) \neq 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. - published version (18p)

Bib entry

@article{Sh:418, author = {Mekler, Alan H. and Shelah, Saharon}, title = {{Every coseparable group may be free}}, journal = {Israel J. Math.}, fjournal = {Israel Journal of Mathematics}, volume = {81}, number = {1-2}, year = {1993}, pages = {161--178}, issn = {0021-2172}, mrnumber = {1231184}, mrclass = {20K40 (03E35 03E55 03E75 20A15)}, doi = {10.1007/BF02761303}, note = {\href{https://arxiv.org/abs/math/9305205}{arXiv: math/9305205}}, arxiv_number = {math/9305205} }