Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-24T13:38:20.516Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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.)

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