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
  • Home
Hostname: page-component-559fc8cf4f-s5ss2 Total loading time: 1.827 Render date: 2021-02-25T05:31:18.445Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
The Journal of Symbolic Logic The Journal of Symbolic Logic

Article contents

The strength of the isomorphism property

Published online by Cambridge University Press:  12 March 2014

Renling Jin  and
Saharon Shelah
Renling Jin
Affiliation:
Department of Mathematics, University of of California, Berkeley, California 94720
Saharon Shelah
Affiliation:
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

In § 1 of this paper, we characterize the isomorphism property of nonstandard universes in terms of the realization of some second-order types in model theory. In §2, several applications are given. One of the applications answers a question of D. Ross in [this Journal, vol. 55 (1990), pp. 1233–1242] about infinite Loeb measure spaces.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 1 , March 1994 , pp. 292 - 301
Copyright
Copyright © Association for Symbolic Logic 1994

Access options

Get access to the full version of this content by using one of the access options below.
If you should have access and can't see this content please contact technical support.

References

[CK] Chang, C. C. and Keisler, H. J., Model Theory, North-Holland, Amsterdam, 1983; third edition, 1990.Google Scholar
[H1] Henson, C. W., The isomorphism property in nonstandard analysis and its use in the theory of Banach space, this Journal, vol. 39 (1974), pp. 717–731.Google Scholar
[H2] Henson, C. W., When do two Banach spaces have isometrically isomorphic nonstandard hulls, Israel Journal of Mathematics, vol. 22 (1975), pp. 57–67.CrossRefGoogle Scholar
[H3] Henson, C. W., Unbounded Loeb measures, Proceedings of the American Mathematical Society, vol. 74 (1979), pp. 143–150.CrossRefGoogle Scholar
[J1] Jin, R., The isomorphism property versus the special model axiom, this Journal, vol. 57 (1992), pp. 975–987.Google Scholar
[J2] Jin, R., A theorem on the isomorphism property, this Journal, vol. 57 (1992), pp. 1011–1017.Google Scholar
[JK] Jin, R. and Keisler, H. J., Game sentences and ultrapowers, Annals of Pure and Applied Logic, vol. 60 (1993), pp. 261–274.CrossRefGoogle Scholar
[L] Loeb, P., Conversion from nonstandard to standard measure space and applications in probability theory, Transactions of the American Mathematical Society, vol. 211 (1975), pp. 113–122.CrossRefGoogle Scholar
[R] Ross, D., The special model axiom in nonstandard analysis, this Journal, vol. 55 (1990), pp. 1233–1242.Google Scholar
[S] Shelah, S., Every two elementarily equivalent models have isomorphic ultrapowers, Israel Journal of Mathematics, vol. 10 (1971), pp. 224–233.CrossRefGoogle Scholar
[SB] Stroyan, K. D. and Bayod, J. M., Foundation of Infinitesimal Stochastic Analysis, North-Holland, Amsterdam, 1986.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 5 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 25th February 2021. This data will be updated every 24 hours.

4 Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@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 sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent 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.

The strength of the isomorphism property
Available formats
×

Send article to Dropbox

To send 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 use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

The strength of the isomorphism property
Available formats
×

Send article to Google Drive

To send 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 use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

The strength of the isomorphism property
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *