Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-02T19:45:06.998Z Has data issue: false hasContentIssue false

Expansions of models of ω-stable theories

Published online by Cambridge University Press:  12 March 2014

Steven Buechler*
Affiliation:
Yale University, New Haven, Connecticut 06520

Abstract

We prove that every relation-universal model of an ω-stable theory is saturated. We also show there is a large class of ω-stable theories for which every resplendent model is homogeneous.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1984

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

[BS]Barwise, J. and Schlipf, J., An introduction to recursively saturated and resplendent models, this Journal, vol. 41 (1976), pp. 531536.Google Scholar
[Ba1]Baldwin, J., Manuscript for a book on stability theory (to be published by Springer-Verlag).Google Scholar
[Ba2]Baldwin, J., Definability and the hierarchy of stable theories, Logic Year 1979/80 (Proceedings of Seminars and Conference, Storrs, Connecticut, 1979/80), Lecture Notes in Mathematics, vol. 859, Springer-Verlag, Berlin, 1981, pp. 115.Google Scholar
[CK]Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam, 1972.Google Scholar
[KL]Knight, J. and Lachlan, A. H., Recursive definability in ω-stable theories of finite rank, preprint, 1982.Google Scholar
[Kt]Knight, J., Theories whose resplendent models are homogeneous, Israel Journal of Mathematics, vol. 42 (1982), pp. 151161.CrossRefGoogle Scholar
[Ku]Kueker, D. W., Generalized interpolation and definability, Annals of Mathematical Logic, vol. 1 (1970), pp. 423468.CrossRefGoogle Scholar
[LP]Lascar, D. and Poizat, B., An introduction to forking, this Journal, vol. 44 (1979), pp. 330350.Google Scholar
[Sa]Sacks, G., Saturated model theory, Benjamin, Reading, Massachusetts, 1972.Google Scholar
[Sc]Schlipf, J., A guide to the identification of admissible sets above structures, Annals of Mathematical Logic, vol. 12 (1977), pp. 151192.CrossRefGoogle Scholar
[Sh]Shelah, S., Classification theory and the number of nonisomorphic models, North-Holland, Amsterdam, 1978.Google Scholar