Skip to main content
Springer Nature Link
Log in

The Weak Ultrafilter Axiom

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

Abstract

The main theorem is that the Ultrafilter Axiom of Woodin (J Math Log 11(2):115–37, 2011) must fail at all cardinals where the Axiom I0 holds, in all non-strategic extender models subject only to fairly general requirements on the non-strategic extender model.

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. Feng, Q., Magidor, M., Woodin, W.H. : Universally Baire sets of reals. In: Judah, H., Just, W., Woodin, H. (eds.) Set Theory of the Continuum, Volume 26 of Mathematical Sciences Research Institute Publications, pp. 203–242. Springer, Heidelberg (1992)

  2. Larson P.: The Stationary Tower: Notes on a Course by W. Hugh Woodin. University Lecture Series, American Mathematical Society, Providence (2004)

    Google Scholar 

  3. Martin D.A., Steel J.: Iteration trees. J. Am. Math. Soc. 7, 1–74 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Neeman I.: Inner models in the region of a Woodin limit of Woodin cardinals. Ann. Pure Appl. Log. 116(1–3), 67–155 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Woodin W.H.: Suitable extender models I. J. Math. Log. 10(1–2), 101–341 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Woodin W.H.: Suitable extender models II: beyond ω-huge. J. Math. Log. 11(2), 115–437 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Woodin, W.H.: The weak Ultimate-L Conjecture. In: Infinity, computability, and metamathematics. Volume 23 of Tributes, pp. 309–329. College Publications, London (2014)

  8. Woodin, W.H.: Fine structure at the finite levels of supercompactness, preprint (2015, submitted)

Download references

Author information

Authors and Affiliations

  1. Harvard University, Cambridge, MA, USA

    W. Hugh Woodin

Authors
  1. W. Hugh Woodin
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to W. Hugh Woodin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Woodin, W.H. The Weak Ultrafilter Axiom. Arch. Math. Logic 55, 319–351 (2016). https://doi.org/10.1007/s00153-015-0467-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-015-0467-2

Keywords