Skip to main content Accessibility help
×
Home
Hostname: page-component-5c569c448b-r8t2r Total loading time: 0.266 Render date: 2022-07-06T11:50:02.328Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Two consistency results on set mappings

Published online by Cambridge University Press:  12 March 2014

Péter Komjáth
Affiliation:
Department of Computer Science, Eötvös University, Budapest, Rákóczi Út 5, 1088, Hungary, E-mail: kope@cs.elte.hu
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail: shelah@math.huji.ac.il

Abstract

It is consistent that there is a set mapping from the four-tuples of ωn into the finite subsets with no free subsets of size tn for some natural number tn. For any n < ω it is consistent that there is a set mapping from the pairs of ωn into the finite subsets with no infinite free sets. For any n < ω it is consistent that there is a set mapping from the pairs of ωn into ωn with no uncountable free sets.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2000

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]Erdős, P., Some remarks on set theory, Proceedings of the American Mathematical Society, vol. 1 (1950), pp. 127141.CrossRefGoogle Scholar
[2]Erdős, P. and Hajnal, A., On the structure of set mappings, Acta Mathematica Academiae Scientifica Hungarica, vol. 9 (1958), pp. 111131.CrossRefGoogle Scholar
[3]Erdös, P., Hajnal, A., Máté, A., and Rado, R., Combinatorial set theory: Partition relations for cardinals, North-Holland, Akadémiai Kiadö, 1984.Google Scholar
[4]Grünwald, G., Egy halmazelméleti tételről, Mathematikai És Fizikai Lapok, vol. 44 (1937), pp. 5153.Google Scholar
[5]Hajnal, A., Proof of a conjecture of S. Ruziewicz, Fundamenta Mathematicae, vol. 50 (1961), pp. 123128.CrossRefGoogle Scholar
[6]Hajnal, A. and Máté, A., Set mappings, partitions, and chromatic numbers, Logic Colloquium '73, Bristol, North-Holland, 1975, pp. 347379.Google Scholar
[7]KomjÁth, P., A set mapping with no infinite free subsets, this Journal, vol. 56 (1991), pp. 304306.Google Scholar
[8]Kuratowski, K., Sur une charactérization des alephs, Fundamenta Mathematicae, vol. 38 (1951), pp. 1417.CrossRefGoogle Scholar
[9]Piccard, S., Sur un problème de M. Ruziewicz de la thÉorie des relations, Fundamenta Mathematicae, vol. 29 (1937), pp. 59.Google Scholar
[10]Ruziewicz, S., Une généralisation d'un théorème de M. Sierpiński, Publications Mathématiques de l'Université de Belgrade, vol. 5 (1936), pp. 2327.Google Scholar
6
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.

Two consistency results on set mappings
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.

Two consistency results on set mappings
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.

Two consistency results on set mappings
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? *