Skip to main content
Log in

On endo-rigid, strongly ℵ1-free abelian groups in ℵ1

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

Abstract

Assuming 2 0<2 1 we prove that there is an endo-rigid strongly ℵ1-free group of power ℵ1.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. U. Avraham and S. Shelah,Isomorphism types of Aronszajn trees, independence results, Ann. Math. Logic, to appear.

  2. K. J. Devlin and S. Shelah,A weak version of ◊ which follows from 2 0<2 1, Israel J. Math.29 (1978), 239–247.

    MATH  MathSciNet  Google Scholar 

  3. M. Dugas, thesis, University of Essen, West Germany, 1979.

    Google Scholar 

  4. P. Eklof and A. Mekler,On constructing indecomposable groups in L, J. Algebra49 (1977), 96–106.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. Fuchs,Infinite Abelian Groups, Vol. I, II, Academic Press, 1970, 1973.

  6. J. Gregory,Higher Souslin trees and the generalized continuum hypothesis, J. Symbolic Logic41 (1976), 663–671.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  8. S. Shelah,On successor of singular cardinals, Proc. A.S.L. Meeting in Mons Aug. 1978,Logic Colloquium 78 (M. Boffa, D. Van Dalen and K. McAloon, eds.), Studies in Logic and the Foundation of Math., Vol. 97, North-Hollánd Publ. Co., Amsterdam, 1979, pp. 357–380.

    Google Scholar 

  9. R. M. Solovay,Real valued measurable cardinals, Proc. Symp. in Pure Math., Vol. XIII, 1 (D. Scott, ed.), Amer. Math. Soc., 1971, pp. 397–428.

Download references

Author information

Authors and Affiliations

Authors

Additional information

The author would like to thank the United States-Israel Binational Science Foundation for supporting this research by Grant 1110. The author thanks Prof. P. Eklof for detecting errors in the manuscript.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shelah, S. On endo-rigid, strongly ℵ1-free abelian groups in ℵ1 . Israel J. Math. 40, 291–295 (1981). https://doi.org/10.1007/BF02761369

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02761369

Keywords

Navigation