Skip to main content
Log in

Chang’s conjecture for ℵω

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

Abstract

We establish, starting from some assumptions of the order of magnitude of a huge cardinal, the consistency of (ℵω+1,ℵω)↠(ω10), as well as of some other transfer properties of the type (κ+,κ)↠(α+,α), where κ is singular.

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

  • [DJK] H.-D. Donder, R. Jensen and B. Koppelberg,Some applications of the core model, inSet Theory and Model Theory Lecture Notes in Math. No. 872, Springer-Verlag, Berlin 1981, pp. 55–97.

    Chapter  Google Scholar 

  • [DK] H.-D. Donder and P. Koepke.On the consistency strength of “accessible” Jonsson cardinals and of the weak Chang Conjecture. Ann. Pure Appl. Logic25 (1983), 233–261.

    Article  MATH  MathSciNet  Google Scholar 

  • [DKL] H.-D. Donder, P. Koepke and J.-P. Levinski, Some stationary subsets ofPλ, Proc. Am. Math. Soc.102 (1988), 1000–1004.

    Article  MATH  MathSciNet  Google Scholar 

  • [DL] H.-D. Donder and J.-P. Levinski,Some principles related to Chang's Conjecture, Ann. Pure Appl. Logic, to appear.

  • [F] M. Foreman,Large cardinals and strong model-theoretic transfer properties, Trans. Am. Math. Soc.272 (1982), 427–463.

    Article  MATH  MathSciNet  Google Scholar 

  • [K] K. Kunen,Saturated ideals, J. Symb. Logic43 (1978), 65–76.

    Article  MATH  MathSciNet  Google Scholar 

  • [L] J.-P. Levinski,Instances of the Conjecture of Chang, Isr. J. Math.48 (1984), 225–243.

    Article  MATH  MathSciNet  Google Scholar 

  • [R] F. Rowbottom,Some strong axioms of infinity incompatible with the axiom of constructibility, Ann. Math. Logic3 (1971), 1–44.

    Article  MATH  MathSciNet  Google Scholar 

  • [S] S. Shelah,Proper Forcing, Lecture Notes in Math. No. 940, Springer-Verlag, Berlin, 1982.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Levinski, JP., Magidor, M. & Shelah, S. Chang’s conjecture for ℵω . Israel J. Math. 69, 161–172 (1990). https://doi.org/10.1007/BF02937302

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02937302

Keywords

Navigation