Skip to main content
Log in

On HOD-supercompactness

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

Abstract

During his Fall 2005 set theory seminar, Woodin asked whether V-supercompactness implies HOD-supercompactness. We show, as he predicted, that that the answer is no.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Hamkins D.J.: Extensions with the approximation and cover properties have no new large cardinals. Fund. Math. 180(3), 257–277 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Jech, T.: Set theory. Springer Monographs in Mathematics. Springer, Berlin. The third millennium edition (2003) (revised and expanded)

  3. Laver R.: Making the supercompactness of κ indestructible under κ-directed closed forcing. Israel J. Math. 29(4), 385–388 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  4. Woodin, H.: Suitable extender sequences (unpublished manuscript)

  5. Woodin H.: Set Theory Seminar Notes. Berkeley, Fall (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Grigor Sargsyan.

Additional information

G. Sargsyan wishes to thank the referee for thoroughly reading the preliminary version of this paper and for making many important suggestions

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sargsyan, G. On HOD-supercompactness. Arch. Math. Logic 47, 765–768 (2008). https://doi.org/10.1007/s00153-008-0106-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-008-0106-2

Keywords

Mathematics Subject Classification (2000)

Navigation