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Every coseparable group may be free

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6, Burnaby, B.C., Canada

    Alan H. Mekler

  2. Institute of Mathematics, The Hebrew University, Jerusalem, Israel

    Saharon Shelah

  3. Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey, USA

    Saharon Shelah

Authors
  1. Alan H. Mekler
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  2. Saharon Shelah
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Additional information

Dedicated to the memory of Alan H. Mekler

Research supported by NSERC. Research on this paper was begun while the first author was visiting the Hebrew University.

Publication #418. Research supported by the BSF.

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Mekler, A.H., Shelah, S. Every coseparable group may be free. Israel J. Math. 81, 161–178 (1993). https://doi.org/10.1007/BF02761303

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  • DOI: https://doi.org/10.1007/BF02761303

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