Skip to main content
Springer Nature Link
Log in

Maximal chains inωω and ultrapowers of the integers

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

Summary

Various questions posed by P. Nyikos concerning ultrafilters on ω and chains in the partial order (ω, <*) are answered. The main tool is the oracle chain condition and variations of it.

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. Abraham, A., Rubin, M., Shelah, S.: On the consistency of some partition theorems for continuous colorings, and structure of ℵ1-dense real order types. Ann. Pure Appl. Logic29, 123–206 (1985)

    Google Scholar 

  2. Blass, A.: Applications of superperfect forcing and its relatives. In: Steprāns, J., Watson, S. (eds.) Set Theory and its Applications. (Lect. Notes Math., vol. 1401, pp. 18–40) Berlin Heidelberg New York: Springer 1989

    Google Scholar 

  3. Dow, A.: Remote points in spaces with π-weight ω1. Fund. Math.74, 197–205 (1984)

    Google Scholar 

  4. Just, W.: A modification of Shelah's oracle-c.c. with applications. Trans. Amer. Math. Soc.321 (2), 621–645 (1990)

    Google Scholar 

  5. Nyikos, P.: Special ultrafilters and cofinal subsets ofωω. (preprint)

  6. Shelah, S.: Proper forcing. Lect. Notes Math.940 (1982)

  7. Steprāns, J.: Combinatorial consequences of adding Cohen reals. Submitted to Proceedings of the 1991 Jerusalem conference. Set Theory of the reals, p. 19

  8. Todorcevic, S.: Partition problems in topology. J. Am. Math. Soc.84 (1989)

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University, Jerusalem, Israel

    Saharon Shelah

  2. Putgers University, N.J., USA

    Saharon Shelah

  3. Department of Mathematics, York University, 4700 Keele Street, M3J 1P3, North York, Ontario, Canada

    Juris Steprāns

Authors
  1. Saharon Shelah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juris Steprāns
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The first author is partially supported by the basic research fund of the Israeli Academy. The second author is partially supported by NSERC and was a guest of Rutgers University while the research on this paper was being done. The authors would also like to thank P. Nyikos for his valuable comments on early versions of this paper. This is number 465 on the first author's list of publications

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shelah, S., Steprāns, J. Maximal chains inωω and ultrapowers of the integers. Arch Math Logic 32, 305–319 (1993). https://doi.org/10.1007/BF01409965

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01409965

Keywords