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-rbfsf Total loading time: 0.492 Render date: 2022-06-28T04:42:04.794Z 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

-sets of reals

Published online by Cambridge University Press:  12 March 2014

Haim Judah  and
Saharon Shelah
Haim Judah
Affiliation:
Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel Universidad Católica de Chile, Santiago, Chile Institute of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Saharon Shelah
Affiliation:
Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel Universidad Católica de Chile, Santiago, Chile Institute of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Get access Rights & Permissions[Opens in a new window]

Abstract

We build models where all -sets of reals are measurable and (or) have the property of Baire and (or) are Ramsey. We will show that there is no implication between any of these properties for -sets of reals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 1 , March 1993 , pp. 72 - 80
Copyright
Copyright © Association for Symbolic Logic 1993

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

[BA]Baumgartner, J., Iterated forcing, Surveys of set theory, London Mathematical Society Lecture Note Series, no. 87, Cambridge University Press, 1983.Google Scholar
[HS]Harrington, L. and Shelah, S., Some exact equiconsistency results in set theory, Notre Dame Journal of Formal Logic, vol. 26 (1985).CrossRefGoogle Scholar
[JU1]Judah, H., -sets of reals, this Journal, vol. 53 (1988), pp. 636–642.Google Scholar
[JU2]Judah, H., Exact consistency results for -sets of reals, preprint.Google Scholar
[JS]Judah, H. and Shelah, S., Martin's axioms, measurability and equiconsistency results, this Journal, vol. 54 (1989), pp. 78–94.Google Scholar
[JS1]Judah, H. and Shelah, S., Souslin forcing, this Journal, vol. 53 (1988), pp. 1188–1207.Google Scholar
[JS2]Judah, H. and Shelah, S., Δ21-sets of reals, Annals of Pure and Applied Logic, vol. 42 (1989).Google Scholar
[JE]Jech, T., Set theory, Academic Press, San Diego, CA.CrossRefGoogle Scholar
[RS]Raisonnier, J. and Stern, J., The strength of measurability hypotheses, Israel Journal of Mathematics, vol. 50(1985).CrossRefGoogle Scholar
[SH]Shelah, S., Proper forcing, Lectures Notes in Mathematics, vol. 940, Springer-Verlag, Berlin and New York.Google Scholar
[SHI]Shelah, S., Can you take Solovay's inaccesible away?, Israel Journal of Mathematics, vol. 48 (1984).CrossRefGoogle Scholar
[SO]Solovay, R. M., A model of set theory in which every set of reals is Lebesgue measurable. Annals of Mathematics, 1970.Google Scholar
[ST1]Stern, J., Generic extensions which do not add random reals. Lecture Notes in Mathematics, vol. 1130, Springer-Verlag, Berlin and New York, 1985.CrossRefGoogle Scholar
[ST2]Stern, J., Regularity properties of definable set of reals, Annals of Pure and Applied Logic, vol. 29 (1985).CrossRefGoogle 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.

-sets of reals
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.

-sets of reals
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.

-sets of reals
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? *