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Israel Journal of Mathematics

, Volume 81, Issue 1–2, pp 161–178 | Cite as

Every coseparable group may be free

  • Alan H. Mekler
  • Saharon Shelah
Article

Abstract

We show that if\(2^{\aleph _0 } \) Cohen reals are added to the universe, then for every reduced non-free torsion-free abelian groupA of cardinality less than the continuum, there is a primep so that Ext p (A,ℤ)≠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.

Keywords

Ground Model Regular Cardinal Empty Condition Stationary Subset Pure Subgroup 
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Copyright information

© Hebrew University 1993

Authors and Affiliations

  • Alan H. Mekler
    • 1
  • Saharon Shelah
    • 2
    • 3
  1. 1.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada
  2. 2.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA

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