Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T01:25:09.671Z Has data issue: false hasContentIssue false
  • English
  • Français

Superdestructibility: A dual to Laver's indestructibility

Published online by Cambridge University Press:  12 March 2014

Joel David Hamkins  and
Saharon Shelah
Joel David Hamkins
Affiliation:
Mathematics 15-215, City University of New York, College of Staten Island, 2800 Victory BLVD, Staten Island, New York 10314, USA, E-mail: [email protected] Institute of Mathematics, The Hebrew University, Jerusalem, Israel
Saharon Shelah
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 80903, USA, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

After small forcing, any <κ-closed forcing will destroy the supercompactness and even the strong compactness of κ.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 2 , June 1998 , pp. 549 - 554
Copyright
Copyright © Association for Symbolic Logic 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Hamkins, Joel David, Small forcing makes any cardinal superdestructible, to appear in this Journal.Google Scholar
[2] Ketonen, Jussi, Strong compactness and other cardinal sins, Annals of Mathematical Logic, vol. 5 (1972), pp. 47–76.Google Scholar
[3] Laver, Richard, Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel Journal of Mathematics, vol, 29 (1978), pp. 385–388.10.1007/BF02761175Google Scholar