# Sh:418

• Mekler, A. H., & Shelah, S. (1993). Every coseparable group may be free. Israel J. Math., 81(1-2), 161–178.
• 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}
}