Skip to main content
SpringerLink
Log in

Applications of the topological representation of the pcf-structure

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

Abstract

We consider simplified representation theorems in pcf-theory and, in particular, we prove that if \({\aleph_{\omega}^{\aleph_{0}} > \aleph_{\omega_{1}}\cdot2^{\aleph_{0}}}\) then there are cofinally many sequences of regular cardinals such that \({\aleph_{\omega_{1}+1}}\) is represented by these sequences modulo the ideal of finite subsets, using a topological approach to the pcf-structure.

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

Access this article

Log in via an institution

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. Bagaria J.: Locally generic Boolean algebras and cardinal sequences. Algebra Universalis 47, 283–302 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baumgartner J.E., Shelah S.: Remarks on superatomic Boolean algebras. Ann. Pure Appl. Logic 33, 109–129 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bonnet R., Rubin M.: On well-generated Boolean algebras. Ann. Pure Appl. Logic 105, 1–50 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Burke M.R., Magidor M.: Shelah’s pcf theory and its applications. Ann. Pure Appl. Logic 50, 207–254 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dow A., Watson S.: Skula spaces. Comment. Math. Univ. Carolin. 31(n1), 27–31 (1990)

    MATH  MathSciNet  Google Scholar 

  6. Foreman, M., Laflamme, C., Todorcevic, S.: Singular Cardinals Combinatorics. http://www.pims.math.ca/birs/workshops/2004/04w5523/report0w5523.pdf

  7. Holz, M., Steffens, K., Weitz, E.: Introduction to Cardinal Arithmetic. In: Birkhäuser Advanced Texts. Birkhäuser, Basel (1999)

  8. Jech, T.: Set Theory. The Third Millenium Edition. In: Springer Monographs in Mathematics. Springer, Berlin (2003)

  9. Koepke P., Martinez J.C.: Superatomic Boolean algebras constructed from morasses. J. Symb. Logic 60, 940–951 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ruyle, J.: Cardinal Sequences of Pcf Structures, Ph.D. Thesis, University of California, Riverside, September 1998

  11. Shelah, S.: Cardinal arithmetic. In: Oxford Logic Guides, vol. 29. Clarendon Press, Oxford (1994)

  12. Stephenson Jr., R.M.: Initially \({{\kappa}}\) -compact spaces and related spaces. In:Kunen, K.,Vaughan, J.E. (eds.) Handbook of Set-Theoretic Topology. North-Holland Publishing Co., Amsterdam, pp. 603–632 (1984)

    Google Scholar 

  13. Todorcevic, S.: A remark on superatomic Boolean algebras, unpublished note, November 1981

Download references

Author information

Authors and Affiliations

  1. Equipe de Logique Mathématique, UFR de Mathématiques (case 7012), Université Denis-Diderot Paris 7, 2 place Jussieu, 75251, Paris Cedex 05, France

    Luís Pereira

Authors
  1. Luís Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luís Pereira.

Additional information

Supported by the Portuguese Foundation for Science and Technology, ref. BD\16650\2004.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pereira, L. Applications of the topological representation of the pcf-structure. Arch. Math. Logic 47, 517–527 (2008). https://doi.org/10.1007/s00153-008-0098-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-008-0098-y

Keywords

Mathematics Subject Classification (2000)

Search

Navigation