Skip to main content
SpringerLink
Log in

Whitehead groups may not be free even assuming ch, II

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We prove some theorems on uncountable abelian groups, and consistency results promised in the first part, and also that a variant of \( \diamondsuit _{\omega _1 } \) called ♣ (club), is consistent with 2ℵ 0<ℵ1.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. E. Baumgartner,Almost disjoint sets, the dense set problem and the partition calculus, Ann. Math. Logic9 (1976), 187–272.

    Article  MATH  MathSciNet  Google Scholar 

  2. K. Devlin,Aspects of Constructibility, Springer Verlag Lecture Notes in Math.354, 1973.

  3. K. Devlin and S. Shelah,A weak version of the diamond follows from 2ℵ 0 <2ℵ1, Israel J. Math.29 (1978), 239–247.

    MATH  MathSciNet  Google Scholar 

  4. L. Fuchs,Infinite Abelian Groups, Academic Press, New York, London, Vol. I, 1970; Vol. II, 1973.

    MATH  Google Scholar 

  5. H. L. Hiller and S. Shelah,Singular cohomology in L, Israel J. Math.26 (1977), 313–319.

    Article  MATH  MathSciNet  Google Scholar 

  6. T. Jech,Set Theory, Academic Press, New York, 1978.

    Google Scholar 

  7. S. Shelah,Infinite abelian groups, Whitehead problem and some constructions, Israel J. Math.18 (1974), 243–256.

    MATH  MathSciNet  Google Scholar 

  8. S. Shelah,Whitehead groups may not be free even assuming CH, I, Israel J. Math.28 (1977), 193–203.

    Article  MATH  MathSciNet  Google Scholar 

  9. S. Shelah,On uncountable abelian groups, Israel J. Math.32 (1979), 311–330.

    MATH  MathSciNet  Google Scholar 

  10. S. Shelah,A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals, Israel J. Math.21 (1975), 319–349.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Saharon Shelah

  2. Department of Mathematics, University of California, Berkeley, California, USA

    Saharon Shelah

Authors
  1. Saharon Shelah
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author would like to thank the United States-Israel Binational Science Foundation for Grant 1110 and the NSF for Grant MCS-08479.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shelah, S. Whitehead groups may not be free even assuming ch, II. Israel J. Math. 35, 257–285 (1980). https://doi.org/10.1007/BF02760652

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02760652

Keywords

Search

Navigation