Skip to main content Accessibility help
×
Home
Hostname: page-component-5c569c448b-6g96d Total loading time: 0.372 Render date: 2022-07-06T11:54:06.462Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Diamonds, uniformization

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Affiliation:
The Hebrew University, Jerusalem, Israel University of California, Berkeley, California 94720

Abstract

Assume G.C.H. We prove that for singular λ, □λ implies the diamonds hold for many S ⊆ λ+ (including S ⊆ {δ:δ ∈ λ+, cf δ = cf λ}.) We also have complementary consistency results.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1984

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

[DS]Devlin, K. and Shelah, S., A weak form of the diamond which follows from 20 < 21, Israel Journal of Mathematics, vol. 29 (1978), pp. 239247.CrossRefGoogle Scholar
[DJ]Devlin, K. and Johnsbråten, H., The Souslin problem, Lecture Notes in Mathematics, vol. 405, Springer-Verlag, Berlin, 1974.Google Scholar
[Gr]Gregory, J., Higher Souslin trees, this Journal, vol. 41 (1976), pp. 663671.Google Scholar
[J]Jensen, R. B., The fine structure of the constructible universe. Annals of Mathematical Logic, vol. 4 (1972), pp. 229308.CrossRefGoogle Scholar
[K]Keisler, H. J., Models with tree structures, Proceedings of the Tarski Symposium (Berkeley, 1971; Henkin, L., editor), Proceedings of Symposia in Pure Mathematics, vol. 25, American Mathematical Society, Providence, R.I., 1974, pp. 331348.CrossRefGoogle Scholar
[Sh1]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar
[Sh2]Shelah, S., Whitehead groups may not be free even assuming CH. I, Israel Journal of Mathematics, vol. 28 (1977), pp. 193203.CrossRefGoogle Scholar
[Sh3]Shelah, S., On successors of singular cardinals, Logic Colloquium '78 (Boffa, M., van Dalen, D. and McAloon, K., editors), Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam. 1979, pp. 357380.Google Scholar
[Sh4]Shelah, S., Whitehead groups may not be free even assuming CH. II, Israel Journal of Mathematics, vol. 35 (1980), pp. 257285.CrossRefGoogle Scholar
[SK]Steinhorn, C.J. and King, J. H., The uniformization property for ℵ2, Israel Journal of Mathematics, vol. 36 (1980), pp. 248256.CrossRefGoogle Scholar
36
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.

Diamonds, uniformization
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.

Diamonds, uniformization
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.

Diamonds, uniformization
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? *