Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T21:35:55.557Z Has data issue: false hasContentIssue false
  • English
  • Français

On uniqueness of prime models

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Saharon Shelah*
Affiliation:
Hebrew University, Jerusalem, Israel University of Wisconsin, Madison, Wisconsin 53706
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove there are theories (stable or countable) for which over every A there is a prime model but it is not necessarily unique. We also give a simplified proof of the uniqueness theorem for countable stable theories.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 44 , Issue 2 , June 1979 , pp. 215 - 220
Copyright
Copyright © Association for Symbolic Logic 1979

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

REFERENCES

[CK]Chang, C.C. and Keisler, H. T., Model theory, North-Holland, Amsterdam, 1973.Google Scholar
[Sa]Sacks, G., Saturated model theory, Benjamin, Reading, Massachusetts, 1970.Google Scholar
[Sh 1]Shelah, S., Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam.Google Scholar
[Sh 2]Shelah, S., The lazy model-theorist's guide to stability, Proceedings of a Symposium on Model Theory, Louvain, 1975, Logique et Analyse, 71/72(1975), pp. 241–308.Google Scholar
[Sh 2]Shelah, S., Uniqueness and characterization of prime models over sets for totally transcendental theories, this Journal, vol. 37 (1972), pp. 107–113. Six days of model theory (P. Henrard, Editor), Editions Cortela 1661, Albeuve, Switzerland, 1978.Google Scholar
[V]Vaught, R.L., Denumerable models of complete theories, Infinistic methods, Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 1959, Pergamon Press, London and Panstwowe, Wydawnictwo Naukowe, Warsaw, 1961, pp. 303–321.Google Scholar