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The stability function of a theory1

Published online by Cambridge University Press:  12 March 2014

H. Jerome Keisler
H. Jerome Keisler*
Affiliation:
University of Wisconsin, Madison, WI 53706
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Abstract

Let T be a complete theory with infinite models in a countable language. The stability function gT(κ) is defined as the supremum of the number of types over models of T of power κ. It is proved that there are only six possible stability functions, namely κ, κ + 2ω, κω, ded κ, (ded κ)ω, 2κ.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 43 , Issue 3 , September 1978, pp. 481 - 486
Copyright
Copyright © Association for Symbolic Logic 1978

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Footnotes

1

This research was supported in part by NSF Grant MCS76–06541. The author is a John Simon Guggenheim Fellow.

References

REFERENCES

[1]Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam, 1973.Google Scholar
[2]Erdös, P. and Makkai, M., Some remarks on set theory, X, Studia Scientiarum Mathematicarum Hungarica, vol. 1 (1966), pp. 157–159.Google Scholar
[3]Keisler, H. J., The number of types in a first order theory, Notices of the American Mathematical Society, vol. 21 (1974), p. A–316.Google Scholar
[4]Keisler, H. J., Six classes of theories, Journal of the Australian Mathematical Society, vol. 21 (1976), Series A, pp. 257–266.CrossRefGoogle Scholar
[5]Morley, M., Categoricity in power, Transactions of the American Mathematical Society, vol. 144 (1965), pp. 514–538.CrossRefGoogle Scholar
[6]Shelah, S., Stability, the finite cover property, and superstability, Annals of Mathematical Logic, vol. 3 (1971), pp. 271–362.CrossRefGoogle Scholar