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On uniqueness of prime models

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Affiliation:
Hebrew University, Jerusalem, Israel University of Wisconsin, Madison, Wisconsin 53706

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
Copyright
Copyright © Association for Symbolic Logic 1979

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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. 241308.Google Scholar
[Sh 2]Shelah, S., Uniqueness and characterization of prime models over sets for totally transcendental theories, this Journal, vol. 37 (1972), pp. 107113. 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. 303321.Google Scholar
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