Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
Hostname: page-component-558cb97cc8-fjc52 Total loading time: 0.378 Render date: 2022-10-06T09:03:14.414Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": true, "useSa": true } hasContentIssue true
  • English
The Journal of Symbolic Logic The Journal of Symbolic Logic

Article contents

Regular ultrafilters and finite square principles

Published online by Cambridge University Press:  12 March 2014

Juliette Kennedy ,
Saharon Shelah  and
Jouko Väänänen
Juliette Kennedy
Affiliation:
Department of Philosophy, Utrecht University, Netherlands Department of Mathematics and Statistics, University of Helsinki, Finland, E-mail: jkennedy@cc.helsinki.fi
Saharon Shelah
Affiliation:
Department of Philosophy, Utrecht University, Netherlands Institute of Mathematics, Hebrew University, Jerusalem, Israel, E-mail: shelah@math.huji.ac.il
Jouko Väänänen
Affiliation:
Department of Philosophy, Utrecht University, Netherlands Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, Netherlands, E-mail: jouko.vaananen@helsinki.fi
Get access Rights & Permissions[Opens in a new window]

Abstract

We show that many singular cardinals λ above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle introduced in [3]. For such ultrafilters D and cardinals λ there are models of size λ for which Mλ/D is not λ++-universal and elementarily equivalent models M and N of size λ for which Mλ/D and Nλ/D are non-isomorphic. The question of the existence of such ultrafilters and models was raised in [1].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 3 , September 2008 , pp. 817 - 823
Copyright
Copyright © Association for Symbolic Logic 2008

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]Chang, C. C. and Keisler, J., Model theory, North-Holland, 1990.Google Scholar
[2]Jensen, R., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308, erratum, R. Jensen, The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), p. 443, with a section by Jack Silver.CrossRefGoogle Scholar
[3]Kennedy, J. and Sheiah, S., On regular reduced products, this Journal, vol. 67 (2002), no. 3, pp. 1169–1177.Google Scholar
[4]Kennedy, J. and Sheiah, S., More on regular reduced products, this Journal, vol. 69 (2004), no. 4, pp. 1261–1266.Google Scholar
[5]Magidor, M. and Shelah, S., The tree property at successors of singular cardinals, Archive for Mathematical Logic, vol. 35 (1996), no. 5-6, pp. 385–404.CrossRefGoogle Scholar
[6]Shelah, S., “Gap 1” two-cardinal principles and the omitting types theorem for L(Q), Israel Journal of Mathematics, vol. 65 (1989), no. 2, pp. 133–152.CrossRefGoogle Scholar
4
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.

Regular ultrafilters and finite square principles
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.

Regular ultrafilters and finite square principles
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.

Regular ultrafilters and finite square principles
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? *