Skip to main content Accessibility help
×
Home
Hostname: page-component-559fc8cf4f-6pznq Total loading time: 0.257 Render date: 2021-02-25T04:32:47.498Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Isomorphic but not lower base-isomorphic cylindric set algebras

Published online by Cambridge University Press:  12 March 2014

B. Biró
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, H-1364 Budapest, Hungary
S. Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel

Abstract

This paper belongs to cylindric-algebraic model theory understood in the sense of algebraic logic. We show the existence of isomorphic but not lower base-isomorphic cylindric set algebras. These algebras are regular and locally finite. This solves a problem raised in [N 83] which was implicitly present also in [HMTAN 81]. This result implies that a theorem of Vaught for prime models of countable languages does not continue to hold for languages of any greater power.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1988

Access options

Get access to the full version of this content by using one of the access options below.

References

[AN 81]Andréka, H. and Németi, I., Oncylindric-relativized set algebras, [HMTAN 81], pp. 131315.Google Scholar
[B 85]Biró, B., Isomorphic but not base-isomorphic base-minimal cylindric algebras, Algebra Universalis (to appear).Google Scholar
[B 86]Biró, B., Lower base-isomorphisms of relation algebras and cylindric algebras, manuscript, Mathematical Institute of the Hungarian Academy of Sciences, Budapest.Google Scholar
[B 86a]Biró, B., Isomorphic but not lower base-isomorphic cylindric algebras of finite dimension, Notre Dame Journal of Formal Logic (to appear).Google Scholar
[B 87]Biró, B., Isomorphism does not imply base-isomorphism for cylindric algebras that are not locally finite or not regular, Commentationes Mathematicae Universitatis Carolinae, vol. 28 (1987), pp. 221226.Google Scholar
[ChK 73]Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam.Google Scholar
[HMT 71]Henkin, L., Monk, J. D. and Tarski, A., Cylindric algebras. Part I, North-Holland, Amsterdam.Google Scholar
[HMT 81]Henkin, L., Cylindric set algebras and related structures, [HMTAN 81], pp. 1129.Google Scholar
[HMT 85]Henkin, L., Cylindric algebras. Part II, North-Holland, Amsterdam.Google Scholar
[HMTAN 81]Henkin, L., Monk, J. D., Tarski, A., Andréka, H. and Németi, I., Cylindric set algebras, Lecture Notes in Mathematics, vol. 883, Springer-Verlag, Berlin.Google Scholar
[L 85]Larson, J., The number of one-generated cylindric set algebras of dimension greater than two, this Journal, vol. 50, pp. 5971.Google Scholar
[M 76]Monk, J. D., Mathematical logic, Springer-Verlag, Berlin.CrossRefGoogle Scholar
[N 83]Németi, I., Cylindric relativised set algebras and Boolean algebras with operators have SAP; which lead lo notes on algebraic model theory. Preprint No. 1983/4, Mathematical Institute of the Hungarian Academy of Sciences, Budapest.Google Scholar
[S 83]Serény, G., On regular locally finite-dimensional cylindric set algebras with atomic neat reducts, preprint, Polytechnical University of Budapest.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: 6 *
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.

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.

Isomorphic but not lower base-isomorphic cylindric set algebras
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.

Isomorphic but not lower base-isomorphic cylindric set algebras
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.

Isomorphic but not lower base-isomorphic cylindric set algebras
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *