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On theories T categorical in |T|

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Saharon Shelah*
Affiliation:
The Hebrew University of Jerusalem
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Abstract

Morley conjectured that if an infinite first-order theory T is categorical in the power |T| > ℵ0, then it has a model of power < |T| Here we affirm this conjecture for the case |T|ℵ0=|T|.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 1 , March 1970 , pp. 73 - 82
Copyright
Copyright © Association for Symbolic Logic 1970

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Footnotes

1

I would like to thank my friend Leo Marcus for translating this paper and finding many errors. I would like to thank Mr. Victor Harnik for suggesting the simplified proof of Theorem 6.2, which appears here.

References

[1] Frayne, T., Morel, A. and Scott, D., Reduced direct products, Fundamenta mathematicae, vol. 51 (1962), pp. 195–248.CrossRefGoogle Scholar
[2] Keisler, H. J., Ultraproducts and saturated models, Indagationes mathematicae, vol. 26 (1964), pp. 178–186.CrossRefGoogle Scholar
[3] Morley, M., Categoricity in power, Transactions of the American Mathematical Society, vol. 114 (1965), pp. 514–538.CrossRefGoogle Scholar
[4] Morley, M. and Vaught, R., Homogeneous universal models, Mathematica Scandinavica, vol. 11 (1962), pp. 37–57.CrossRefGoogle Scholar
[5] Ressayre, J. P., Sur les théories du premier ordre categorique en un cardinal, Transactions of the American Mathematical Society, vol. 142 (1969), pp. 481–505.Google Scholar
[6] Shelah, S., Stable theories, Israel journal of mathematics, vol. 7 (1969), No. 3.CrossRefGoogle Scholar
[7] Shelah, S., Finite diagrams stable in power, Annals of mathematical logic (to appear).Google Scholar
[8] Shelah, S., On saturation of ultrapowers (to appear).Google Scholar
[9] Ehrenfeucht, A. and Mostowski, A., Models of axiomatic theories admitting automorphisms, Fundamenta mathematicae, vol. 43 (1956), pp. 50–68.CrossRefGoogle Scholar