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-56f9d74cfd-w6k7h Total loading time: 0.196 Render date: 2022-06-27T06:54:20.319Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }
  • English
The Journal of Symbolic Logic The Journal of Symbolic Logic

Article contents

Successors of singular cardinals and coloring theorems II

Published online by Cambridge University Press:  12 March 2014

Todd Eisworth  and
Saharon Shelah
Todd Eisworth
Affiliation:
Institute of Mathematics, The Hebrew University of JerusalemJerusalem, Israel
Saharon Shelah
Affiliation:
Department of Mathematics, Ohio UniversityAthens, Oh 45701, USA, E-mail: eisworth@math.ohiou.edu Department of Mathematics, Rutgers University, New Brunswick, Nj, USA, E-mail: shelah@math.huji.ac.il
Get access Rights & Permissions[Opens in a new window]

Abstract

In this paper, we investigate the extent to which techniques used in [10], [2], and [3]—developed to prove coloring theorems at successors of singular cardinals of uncountable cofinality—can be extended to cover the countable cofinality case.

Keywords

square-brackets partition relationsminimal walkssuccessor of singular cardinal
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 4 , December 2009 , pp. 1287 - 1309
Copyright
Copyright © Association for Symbolic Logic 2009

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]Baumgarter, James E., A new class of order-types, Annals of Pure and Applied Logic, vol. 54 (1991), no. 3, pp. 195–227.Google Scholar
[2]Eisworth, T. and Shelah, S., Successors of singular cardinals and coloring theorems I, Archive for Mathematical Logic, vol, 44 (2005), no. 5, pp. 597–618.CrossRefGoogle Scholar
[3]Eisworth, Todd, A note on strong negative partition relations, Fundamenta Mathematicae, vol. 202 (2009), pp. 97–123.CrossRefGoogle Scholar
[4]Eisworth, Todd, Successors of singular cardinals, Handbook of set theory (Foreman, Matthew and Kanamori, Akihiro, editors), vol. II, Springer, forthcoming.Google Scholar
[5]Eisworth, Todd, Club-guessing, stationary reflection, and coloring theorems. Annals of Pure and Applied Logic, submitted.Google Scholar
[6]Erdös, P., Hajnal, A., and Rado, R., Partition relations for cardinal numbers, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 16 (1965), pp. 93–196.CrossRefGoogle Scholar
[7]Kojman, Menachem, The ABC of PCF, unpublished manuscript.Google Scholar
[8]Shelah, Saharon, On successors of singular cardinals, Logic Colloquium '78 (Mons, 1978), Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam, 1979, pp. 357–380.Google Scholar
[9]Shelah, Saharon, Cardinal arithmetic, Oxford Logic Guides, vol. 29, Oxford University Press, 1994.Google Scholar
[10]Shelah, Saharon, There are Jonsson algebras in many inaccessible cardinals, Cardinal arithmetic, Oxford Logic Guides, vol. 29, Oxford University Press, 1994, Chapter III.Google Scholar
[11]Todorčević, Stevo, Partitioning pairs of countable ordinals, Acta Mathematica, vol. 159 (1987), no. 3–4, pp. 261–294.CrossRefGoogle Scholar
[12]Todorčević, Stevo, Walks on ordinals and their characteristics, Progress in Mathematics, vol. 263, Birkhauser, 2007.Google Scholar
[13]Todorčević, Stevo, Coherent sequences, Handbook of set theory (Foreman, Matthew and Kanamori, Akihiro, editors), vol. I, Springer, forthcoming.Google Scholar
5
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.

Successors of singular cardinals and coloring theorems II
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.

Successors of singular cardinals and coloring theorems II
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.

Successors of singular cardinals and coloring theorems II
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? *