Israel Journal of Mathematics

, Volume 28, Issue 3, pp 193–204 | Cite as

Whitehead groups may be not free, even assuming CH, I

  • Saharon Shelah


We prove the consistency with ZFC+G.C.H. of an assertion, which implies several consequences of\(MA + 2^{\aleph _0 } > \aleph _1 \), which\(\diamondsuit \aleph _1 \) implies their negation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    U. Avraham and S. Shelah,A generalization of MA consistent with CH, mimeograph, circulated in fall 1975.Google Scholar
  2. 2.
    U. Avraham, K. Devlin and S. Shelah, in preparation.Google Scholar
  3. 3.
    K. Devlin and H. Johnstraten,The Souslin Problem, Springer-Verlag Lecture Notes405, 1974.Google Scholar
  4. 4.
    K. Devlin and S. Shelah,A weak form of ◊ which follows from a weak version of CH, to appear in Israel J. Math.Google Scholar
  5. 4a.
    K. Devlin and S. Shelah,A note on the normal Moore space conjecture, to appear in Canad. J. Math.Google Scholar
  6. 5.
    P. Eklof,Whitehead problem is undecidable, Amer. Math. Monthly 83 (1976), 173–197.CrossRefMathSciNetGoogle Scholar
  7. 6.
    A. Hajnal and A. Mate,Set mappings partitions and chromatic numbers, in Proc. Logic Colloquium, Bristol, 1973 (Rose and Shepherdson, eds.), Studies in Logic and the Foundations of Mathematics, Vol. 80, North-Holland Publ. Co., 1975, pp. 347–380.Google Scholar
  8. 7.
    J. T. Jech,Trees, J. Symbolic Logic36 (1971), 1–14.MATHCrossRefMathSciNetGoogle Scholar
  9. 8.
    D. Martin and R. M. Solovay,Internal Cohen extensions, Ann. Math. Logic,2(1970), 143–178.MATHCrossRefMathSciNetGoogle Scholar
  10. 9.
    S. Shelah,Infinite abelian groups. Whitehead problem and some constructions, Israel J. Math.,18(1974), 243–256.MATHMathSciNetGoogle Scholar
  11. 10.
    S. Shelah,Notes in partition calculus, Vol III (Colloquia Mathematica A Societatis Janos Bolayi 10), to Paul Erdös on his 60th birthday (A. Hajnal, R. Rodo and V. T. Sos, eds.), North-Holland Publ. Co., Amsterdam, London, 1975, pp. 1257–1276.Google Scholar
  12. 11.
    S. Shelah,Two theorems on abelian groups, in preparation.Google Scholar
  13. 12.
    S. Shelah,Whitehead group may not be free, even assuming CH, II, in preparation.Google Scholar
  14. 13.
    S. Shelah,Whitehead problem under CH and other results, Notices Amer. Math. Soc.23(1976), A-650.Google Scholar
  15. 14.
    R. M. Solovay and S. Tennenbaum,Iterated Cohen extensions and Souslin’s problem, Ann. of Math.94(1971), 201–245.CrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1977

Authors and Affiliations

  • Saharon Shelah
    • 1
  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

Personalised recommendations