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-dpvgk Total loading time: 0.322 Render date: 2022-06-25T21:43:15.561Z 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

Coding with ladders a well ordering of the reals

Published online by Cambridge University Press:  12 March 2014

Uri Abraham  and
Saharon Shelah
Uri Abraham
Affiliation:
Department of Mathematics and Computer Science, Ben-Gurion University, Be'er-Sheva, Israel, E-mail: abraham@cs.bgu.ac.il
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail: shelah@math.huji.ac.il
Get access Rights & Permissions[Opens in a new window]

Abstract

Any model of ZFC + GCH has a generic extension (made with a poset of size ℵ2) in which the following hold: there exists a-well ordering of the reals, The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on ω1. Therefore, the study of such ladders is a main concern of this article.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 2 , June 2002 , pp. 579 - 597
Copyright
Copyright © Association for Symbolic Logic 2002

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]Abraham, U., Proper forcing, Handbook of set theory (Foreman, , Kanamori, , and Magidor, , editors).Google Scholar
[2]Abraham, U. and Shelah, S., A Δ22 well-order of the reals and incompactness of L(QMM), Annals of Pure and Applied Logic, vol. 59 (1993), pp. 1–32.CrossRefGoogle Scholar
[3]Abraham, U. and Shelah, S., Martin's axiom and Δ12 well-ordering of the reals, Archive for Mathematical Logic, vol. 35 (1996), pp. 287–298.CrossRefGoogle Scholar
[4]Harrington, L., Long projective well-orderings, Annals of Mathematical Logic, vol. 12 (1977), pp. 1–24.CrossRefGoogle Scholar
[5]Jensen, R. B. and Solovay, R. M., Some applications of almost disjoint sets, Mathematical logic and foundation of set theory (Bar-Hillel, Y., editor). North-Holland, Amsterdam, 1970, pp. 84–104.Google Scholar
[6]Shelah, S., Proper and improper forcing, 2nd ed., Springer, 1998.CrossRefGoogle Scholar
[7]Shelah, S. and Woodin, H., Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable, Israel Journal of Mathematics, vol. 70 (1990), pp. 381–394.CrossRefGoogle Scholar
[8]Solovay, R. M., a paper to be published in the Archive.Google Scholar
[9]Woodin, H., Large cardinals and determinacy, in preparation.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.

Coding with ladders a well ordering of the 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.

Coding with ladders a well ordering of the 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.

Coding with ladders a well ordering of the 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? *