Skip to main content Accessibility help
×
Home
Hostname: page-component-559fc8cf4f-8sgpw Total loading time: 0.606 Render date: 2021-03-01T04:13:58.059Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Independence of strong partition relation for small cardinals, and the free-subset problem

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Affiliation:
Hebrew University of Jerusalem, Jerusalem, Israel

Abstract

We prove the independence of a strong partition relation on ℵω, answering a question of Erdös and Hajnal. We then give an almost complete answer to the free subset problem.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1980

Access options

Get access to the full version of this content by using one of the access options below.

References

[Eh 1]Erdös, P. and Hajnal, A., Unsolved problems in set theory, U.C.L.A. Symposium, 1967; (Scott, , Editor), Proceedings of Symposia in Pure Mathematics, Vol. XII, Part I, American Mathematical Society, Providence, R.I., 1971, pp. 1748.Google Scholar
[EH 2]Erdös, P. and Hajnal, A., Unsolved and solved problems in set theory, Tarski 70th Birthday Symposium, Berkeley, 1971 (Henkin, , Editor), Proceedings of Symposia in Pure Mathematics, Vol. XXV, American Mathematical Society, Providence, R.I., 1974, pp. 269288.Google Scholar
[EH 3]Erdös, P. and Hajnal, A., On a problem of B. Jonsson, Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 14 (1966), pp. 1923.Google Scholar
[EHMR]Erdös, P., Hajnal, A., Mate, A. and Rado, R., Partition calculus (to appear).Google Scholar
[D]Devlin, K., Some weak versions of large cardinal axioms, Annals of Mathematical Logic, vol. 5 (1973), pp. 291325.CrossRefGoogle Scholar
[DP]Devlin, K. and Paris, J., More on the free subset problem, Annals of Mathematical Logic, vol. 5 (1973), pp. 327336.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 4 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 1st March 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@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 sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent 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.

Independence of strong partition relation for small cardinals, and the free-subset problem
Available formats
×

Send article to Dropbox

To send 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 use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Independence of strong partition relation for small cardinals, and the free-subset problem
Available formats
×

Send article to Google Drive

To send 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 use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Independence of strong partition relation for small cardinals, and the free-subset problem
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *