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.
• Version 1993-08-29_10 (19p) published version (18p)

@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}
}