Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-zdfhw Total loading time: 0.325 Render date: 2022-08-15T17:21:19.800Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

The relative consistency of g < cf(Sym(ω))

Published online by Cambridge University Press:  12 March 2014

Heike Mildenbergert*
Affiliation:
The Hebrew University of Jerusalem, Institute of Mathematics, Givat Ram. 91904 Jerusalem., Israel, E-mail: heike@math.huji.ac.il
*
Universität Wien. Institut für Formale Logik. Währinger Str. 25, A-1090, Vienna, Austria, E-mail: heike@logik.univie.ac.at

Abstract

We prove the consistency result from the title. By forcing we construct a model of g = ℵ1, b = cf(Sym(ω)) = ℵ2.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2002

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]Abraham, U.Proper Forcing, Handbook of Set Theory (Foreman, M., Kanamori, A., and Magidor, M., editors), Kluwer, to appear.Google Scholar
[2]Abraham, U., Shelah, S., and Solovay, R., Squared diamonds, Fundamenta Mathematicae, vol. 78 (1982), pp. 165181.Google Scholar
[3]Devlin, K., Constructibility, Omega Series, Springer, 1980.Google Scholar
[4]Kunen, K., Set Theory, An Introduction to Independence Proofs, North-Holland, 1980.Google Scholar
[5]Mathias, A., Happy families, Annals of Mathematical Logic, vol. 12 (1977), pp. 59111.CrossRefGoogle Scholar
[6]Shelah, S., Non-elementary proper forcing notions, Journal of Applied Analysis, submitted.Google Scholar
[7]Shelah, S., Proper and Improper Forcing, Springer, 1977.Google Scholar
[8]Shelah, S., Tree forcings, preprint, 2000.Google Scholar
[9]Thomas, S., Groupwise density and the cofinality of the infinite symmetric group, Archive for Mathematical Logic, vol. 37 (1998), pp. 483493.CrossRefGoogle Scholar
1
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.

The relative consistency of g < cf(Sym(ω))
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.

The relative consistency of g < cf(Sym(ω))
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.

The relative consistency of g < cf(Sym(ω))
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? *