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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.

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

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