Skip to main content
SpringerLink
Log in

Some new upper bounds in consistency strength for certain choiceless large cardinal patterns

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

Summary

In this paper, we show that certain choiceless models of ZF originally constructed using an almost huge cardinal can be constructed using cardinals strictly weaker in consistency strength.

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

  • [An] Andretta, A.: Handwritten notes on extenders

  • [Ap1] Apter, A.: On a problem inspired by determinacy. Isr. J. Math.61, 256–270 (1988)

    Google Scholar 

  • [Ap2] Apter, A.: Some results on consecutive large cardinals. II. Applications of Radin forcing. Isr. J. Math.52, 273–292 (1985)

    Google Scholar 

  • [C1] Cummings, J.: A model in which GCH holds at successors but fails at limits. Trans. Am. Math. Soc. (to appear)

  • [C2] Cummings, J.: Forcing and the arithmetic of small cardinals (to appear)

  • [FW] Foreman, M., Woodin, H.: The GCH can fail everywhere. Ann. Math.133, 1–36 (1991)

    Google Scholar 

  • [G] Gitik, M.: Regular cardinals in models of ZF. Trans. Am. Math. Soc.290, 41–68 (1985)

    Google Scholar 

  • [GS] Gitik, M., Shelah, S.: On certain indestructibility of strong cardinals and a question of Hajnal. Arch. Math. Logic28, 35–42 (1989)

    Google Scholar 

  • [Ma1] Magidor, M.: On the singular cardinals problem. I. Isr. J. Math.28, 1–31 (1977)

    Google Scholar 

  • [Ma2] Magidor, M.: On the singular cardinals problem. II. Ann. Math.106, 517–549 (1977)

    Google Scholar 

  • [Mi1] Mitchell, W.: Sets constructed from sequences of measures revisited. J. Symb. Logic48, 600–609 (1983)

    Google Scholar 

  • [Mi2] Mitchell, W.: The core model for sequences of measures. I. Proc. Cambridge Philos. Soc.95, 229–260 (1984)

    Google Scholar 

  • [MS1] Martin, D.A., Steel, J.: A proof of projective determinacy. J. Am. Math. Soc.2, 71–125 (1989)

    Google Scholar 

  • [MS2] Martin, D.A., Steel, J.: Projective determinacy. Proc. Natl. Acad. Sci. USA85, 6582–6586 (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Baruch College of CUNY, 10010, New York, NY, USA

    Arthur W. Apter

Authors
  1. Arthur W. Apter
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The research for this paper was partially supported by NSF Grant DMS-8616774. In addition, the author would like to thank the referee for comments which considerably helped improve the presentation of the material of this paper

Rights and permissions

Reprints and permissions

About this article

Cite this article

Apter, A.W. Some new upper bounds in consistency strength for certain choiceless large cardinal patterns. Arch Math Logic 31, 201–205 (1992). https://doi.org/10.1007/BF01269948

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01269948

Keywords

Search

Navigation