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On the number of nonisomorphic models of size |T|

Published online by Cambridge University Press:  12 March 2014

Ambar Chowdhury
Ambar Chowdhury*
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, CanadaL8S 4K1,, E-mail:achowdhu@johnny.math.mcmaster.ca
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Abstract

Let T be an uncountable, superstable theory. In this paper we prove

Theorem A. If T has finite rank, then I(|T|, T) ≥ ℵ0.

Theorem B. If T is trivial, then I(|T|, T) ≥ ℵ0.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 1 , March 1994 , pp. 41 - 59
Copyright
Copyright © Association for Symbolic Logic 1994

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References

REFERENCES

[Ba] Baldwin, J., Fundamentals of stability theory, Springer-Verlag, Berlin, Heidelberg, and New York, 1988.CrossRefGoogle Scholar
[BoL] Bouscaren, E. and Lascar, D., Countable models of non-multidimensional ℵ0- stable theories, this Journal, vol. 48 ((983), pp. 197–205.Google Scholar
[B1] Buechler, S., Nontrivial types of U-rank 1, this Journal, vol. 52 (1987), pp. 548–551.Google Scholar
[B2] Buechler, S., The geometry of weakly minimal types, this Journal, vol. 50 (1985), pp. 1044–1053.Google Scholar
[Hr1] Hrushovski, E., Contributions to stable model theory, Ph.D. Thesis, University of California, Berkeley, California, 1986.Google Scholar
[Hr2] Hrushovski, E., Locally modular regular types, Classfication theory, Lecture Notes in Mathematics, vol. 1292, Springer-Verlag, Berlin, Heidelberg, and New York, 1987, pp. 132–164.CrossRefGoogle Scholar
[L1] Lascar, D., Stability in model theory, Longman Scientific and Technical, Louvain, New York, 1987.Google Scholar
[L2] Lascar, D., Relation entre le range U et le poids, Fundamenta Mathematicae, vol. 121, 1984, pp. 117–123.CrossRefGoogle Scholar
[Las] Laskowski, M. C., Uncountable theories that are categorical in a higher power, this Journal, vol. 53 (1988), pp. 512–530.Google Scholar
[LasPR] Laskowski, M. C., Pillay, A., and Rothmaler, P., Tiny models of categorical theories, Archive for Mathematical Logic, vol. 31 (1992), pp. 385–396.Google Scholar
[M] Makkai, M., A survey of basic stability theory, Israel Journal of Mathematics, vol. 49 (1984), pp. 181–238.CrossRefGoogle Scholar
[PR] Pillay, A. and Rothmaler, P., Non-totally transcendental unidimensional theories, Archive for Mathematical Logic, vol. 30 (1990), pp. 93–111.CrossRefGoogle Scholar
[Sa] Saffe, J., Categoricity and ranks, this Journal, vol. 49 (1984), pp. 1379–1382.Google Scholar
[Sh1] Shelah, S., On theories T categorical in | T|, this Journal, vol. 35 (1970), pp. 73–82.Google Scholar
[Sh2] Shelah, S., Classification theory, North-Holland, Amsterdam and New York, 1990.Google Scholar
[ShB] Shelah, S. and Buechler, S., On the existence of regular types, Annals of Pure and Applied Logic, vol. 45 (1989), pp. 207–308.CrossRefGoogle Scholar