Skip to main content
SpringerLink
Log in

The short extenders gap three forcing using a morass

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

Abstract

We show how to construct Gitik’s short extenders gap-3 forcing using a morass, and that the forcing notion is of Prikry type.

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. Devlin, K.: Constructibility, Volume 6 of Perspectives in Mathematical Logic. Springer, Berlin (1984) http://projecteuclid.org/euclid.pl/1235419477

  2. Gitik, M.: Simpler short extenders forcing—gap 3. http://www.math.tau.ac.il/~gitik/gap3.pdf

  3. Gitik M.: Blowing up the power of a singular cardinal. Ann. Pure Appl. Log. 80(1), 17–33 (1996). doi:10.1016/0168-0072(95)00046-1

    Article  MATH  MathSciNet  Google Scholar 

  4. Gitik M.: Blowing up power of a singular cardinal–wider gaps. Ann. Pure Appl. Log. 116(1–3), 1–38 (2002). doi:10.1016/S0168-0072(01)00098-7

    Article  MATH  MathSciNet  Google Scholar 

  5. Gitik M.: On gaps under GCH type assumptions. Ann. Pure Appl. Log. 119(1–3), 1–18 (2003). doi:10.1016/S0168-0072(02)00031-3

    Article  MATH  MathSciNet  Google Scholar 

  6. Gitik, M.: Short extender gap-3 forcing notion. TAU Set theory seminar circulated notes (2008)

  7. Gitik M., Magidor M.: The singular continuum hypothesis revisited. In: Judah, H., Just, W., Hugh Woodin, W. (eds) Set Theory of the Continuum Volume 26 of Mathematical Sciences Research Institute publications, pp. 243–279. Springer, Berlin (1992)

    Google Scholar 

  8. Gitik M., Mitchell W.J.: Indiscernible sequences for extenders, and the singular cardinal hypothesis. Ann. Pure Appl. Log. 82(3), 273–316 (1996). doi:10.1016/S0168-0072(96)00007-3

    Article  MATH  MathSciNet  Google Scholar 

  9. Koszmider P.: Semimorasses and nonreflection at singular cardinals. Ann. Pure Appl. Log. 72, 1–23 (1995). doi:10.1016/0168-0072(93)E0068-Y

    Article  MATH  MathSciNet  Google Scholar 

  10. Koszmider P.: On strong chains of uncountable functions. Israel J. Math. 118(1), 289–315 (2000). doi:10.1007/BF02803525

    Article  MATH  MathSciNet  Google Scholar 

  11. Merimovich, C.: Gitik’s short extender gap-2 forcing notion. TAU Set theory seminar circulated notes (2008)

  12. Merimovich C.: The short extender gap two forcing is of Prikry type. Arch. Math. Log. 48(8), 737–747 (2009). doi:10.1007/s00153-009-0147-1

    Article  MATH  MathSciNet  Google Scholar 

  13. Shelah, S.: Proper and improper forcing volume 5 of Perspectives in Mathematical Logic. Springer (1998) http://projecteuclid.org/euclid.pl/1235419814

  14. Velleman, D.: Simplified morasses. J. Symbol. Log. 49(1), 257–271 (1984) http://projecteuclid.org/euclid.jsl/1183741492

  15. Velleman, D.: Simplified morasses with linear limits. J. Symbol. Log. 49(4), 1001–1021 (1984) http://projecteuclid.org/euclid.jsl/1183741684

    Google Scholar 

  16. Velleman D.: Souslin trees constructed from morasses. In: Baumgartner, J., Martin, D., Shelah, S. (eds) Axiomatic Set Theory Volume 31 of Contemporary Mathematics, pp. 219–241. American Mathematical Society, Providence, RI (1984)

    Google Scholar 

  17. Velleman D.: Simplified gap-2 morasses. Ann. Pure Appl. Log. 34, 171–208 (1987). doi:10.1016/0168-0072(87)90070-4

    Article  MATH  MathSciNet  Google Scholar 

  18. Zwicker W.S.: \({\fancyscript{P}_\kappa\lambda}\) Combinatorics I: statoinary coding sets rationalize the club filter. In: Baumgartner, J., Martin, D., Shelah, S. (eds) Axiomatic Set Theory Volume 31 of Contemporary Mathematics, pp. 243–259. American Mathematical Society, Providence, RI (1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Tel-Aviv Academic College, Rabenu Yeroham St., 68182, Tel-Aviv, Israel

    Carmi Merimovich

Authors
  1. Carmi Merimovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carmi Merimovich.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Merimovich, C. The short extenders gap three forcing using a morass. Arch. Math. Logic 50, 115–135 (2011). https://doi.org/10.1007/s00153-010-0204-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-010-0204-9

Keywords

Mathematics Subject Classification (2000)

Search

Navigation