Skip to main content
Springer Nature Link
Log in

Simplified RCS iterations

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

Summary

We give a simplified treatment of revised countable support (RCS) forcing iterations, previously considered by Shelah (see [Sh, Chap. X]). In particular we prove the fundamental theorem of semi-proper forcing, which is due to Shelah: any RCS iteration of semi-proper posets is semi-proper.

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

  • [B] Baumgartner, J.: Iterated Forcing. In: Mathias, A.R.D. (ed.) Surveys in set theory. (Lond. Math. Soc. Lect. Note Ser. vol.87, pp. 1–59). Cambridge: Cambridge University Press 1983

    Google Scholar 

  • [FMS] Foreman, M., Magidor, M., Shelah, S.: Martin's Maximum, saturated ideals, and non-regular ultrafilters I. Ann. Math.127, 1–47 (1988)

    Google Scholar 

  • [F] Fuchs, U.: Donder's version of revised countable support.

  • [GiSh] Gitik, M., Shelah, S.: On theI-condition. Isr. J. Math.48, 148–158 (1984)

    Google Scholar 

  • [J] Jech, T.: Set theory. New York: Academic Press 1978

    Google Scholar 

  • [K] Kunen, K.: Set theory. An introduction to independence proofs. Amsterdam: North-Holland 1980

    Google Scholar 

  • [S] Schlindwein, C.: Consistency of Suslin's hypothesis, a non-special Aronszajn tree, and GCH. J. Symb. Logic (to appear)

  • [Sh] Shelah, S.: Proper forcing. Lect. Notes Math.940 (1982)

  • [Sh 87] Shelah, S.: Semiproper forcing axiom implies Martin maximum but notPFA +. J. Symb. Log.52, 360–367 (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, 16802, University Park, PA, USA

    Chaz Schlindwein

Authors
  1. Chaz Schlindwein
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schlindwein, C. Simplified RCS iterations. Arch Math Logic 32, 341–349 (1993). https://doi.org/10.1007/BF01409967

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01409967

Keywords