Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-5zjcf Total loading time: 0.284 Render date: 2022-08-15T17:22:48.712Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Superdestructibility: A dual to Laver's indestructibility

Published online by Cambridge University Press:  12 March 2014

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: hamkins@integral.math.csi.cuny.edu Institute of Mathematics, The Hebrew University, Jerusalem, Israel
Saharon Shelah
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 80903, USA, E-mail: shelah@math.huji.ac.il

Abstract

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

Type
Research Article
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

[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. 4776.Google Scholar
[3] Laver, Richard, Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel Journal of Mathematics, vol, 29 (1978), pp. 385388.10.1007/BF02761175Google Scholar
9
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Superdestructibility: A dual to Laver's indestructibility
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Superdestructibility: A dual to Laver's indestructibility
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Superdestructibility: A dual to Laver's indestructibility
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *