Skip to main content
Log in

On the free subset property at singular cardinals

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

We give a proof ofTheorem 1. Let κ be the smallest cardinal such that the free subset property Fr ω (κ,ω 1)holds. Assume κ is singular. Then there is an inner model with ω1 measurable cardinals.

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. Devlin, K.: Some weak versions of large cardinal axioms. Ann. Math. Logic5, 291–325 (1973)

    Google Scholar 

  2. Devlin, K., Paris, J.: More on the free subset problem. Ann. Math. Logic5, 327–336 (1973)

    Google Scholar 

  3. Dodd, A.J.: The core model. (Lond. Math. Soc. Lect. Note Ser. 61) Cambridge, 1982

  4. Koepke, P.: The consistency strength of the free-subset property forω ω . J. Symb. Logic49, 1198–1203 (1984)

    Google Scholar 

  5. Koepke, P.: A theory of short core models and some applications. Doctoral Dissertation, Freiburg (1983)

  6. Koepke, P.: Some applications of short core models. Ann. Pure Appl. Logic37, 179–204 (1988)

    Google Scholar 

  7. Shelah, S.: Independence of strong partition relation for small cardinals, and the free subset property. J. Symb. Logic45, 505–509 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koepke, P. On the free subset property at singular cardinals. Arch Math Logic 28, 43–55 (1989). https://doi.org/10.1007/BF01624082

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01624082

Keywords

Navigation