Skip to main content
Springer Nature Link
Log in

Stationary Cardinals

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

Summary

This paper will define a new cardinal called aStationary Cardinal. We will show that every weakly∏ 11 -indescribable cardinal is a stationary cardinal, every stationary cardinal is a greatly Mahlo cardinal and every stationary set of a stationary cardinal reflects. On the other hand, the existence of such a cardinal is independent of that of a∏ 11 -indescribable cardinal and the existence of a cardinal such that every stationary set reflects is also independent of that of a stationary cardinal. As applications, we will show thatV=L implies ◊ 1 κ holds if κ is∏ 11 -indescribable and so forth.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Baumgartner, J.: Ineffability properties of cardinals. I. In: Infinite and finite Sets. Colloq. Math. Soc. Janos Bolyai 10, pp. 109–130. Kesthely, Hungary, 1973

    Google Scholar 

  2. Baumgartner, J., Taylor, A., Wagon, S.: On splitting stationary subsets of large cardinals. J. Symb. Logic42, 203–214 (1977)

    Google Scholar 

  3. Baumgartner, J.: A new Class of Order Type. Ann. Math. Logic9, 187–222 (1976)

    Google Scholar 

  4. Boos, W.: Boolean extensions which efface the Mahlo properties. J. Symb. Logic39, 254–268 (1974)

    Google Scholar 

  5. Gitik, M., Shelah, S.: Cardinal preserving ideals (to appear)

  6. Harrington, L., Shelah, S.: Some exact equiconsistency results in set theory. Notre Dame J. Formal Logic26, 178–188 (1985)

    Google Scholar 

  7. Jech, T.: Multiple forcing. Cambridge: Cambridge Press 1986

    Google Scholar 

  8. Jech, T., Prikry, K.: Ideals over uncountable sets: application of almost disjoint functions and generic ultrapowers. Mem. Am. Math.18, 214 (1979)

    Google Scholar 

  9. Jensen, R.: The fine structure of the constructible hierarchy. Ann. Math. Logic4, 229–308 (1972)

    Google Scholar 

  10. Johnson, C.: On ideals and stationary reflections. J. Symb. Logic54, 568–575 (1989)

    Google Scholar 

  11. Kunen, K.: Boolean and measurable cardinals. Ann. Math. Logic2, 359–377 (1971)

    Google Scholar 

  12. Leary, C.: Superstationary cardinal and ineffable cardinals. Arch. Math. Logic29, 137–148 (1990) (3)

    Google Scholar 

  13. Magidor, M.: Reflecting stationary sets. J. Symb. Logic47, 755–771 (1982)

    Google Scholar 

  14. Mekler, A.: The consistency strength of Every stationary set reflects. Isr. J. Math.67, 353–366 (1989) (3)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Salem College, 27108, Winston-Salem, NC, USA

    Wenzhi Sun

Authors
  1. Wenzhi Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, W. Stationary Cardinals. Arch Math Logic 32, 429–442 (1993). https://doi.org/10.1007/BF01270466

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01270466

Keywords

Search

Navigation