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Cardinalities of ultraproducts of finite sets

Published online by Cambridge University Press:  12 March 2014

Sabine Koppelberg
Sabine Koppelberg*
Affiliation:
II., Mathematisches Institut der Freien Universität, Berlin, Federal Republic of Germany
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Extract

Keisler, in [1], defined a set F(D) of infinite cardinals for every ultrafilter D on a set I, and, assuming GCH, gave a sufficient condition for a set C of infinite cardinals to have the form F(D) for suitable D and I. In this paper we prove a similar theorem (Theorem 1) under considerably weaker assumptions. Our main tool is a construction of elementary end extensions of Boolean ultrapowers of ω outlined by Shelah in [6, Exercise VI.3.35]. Hence this paper will mostly be concerned with Boolean ultrapowers of ω.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 45 , Issue 3 , September 1980 , pp. 574 - 584
Copyright
Copyright © Association for Symbolic Logic 1980

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References

REFERENCES

[1]Keisler, H. J., Ultraproducts offinite sets, this Journal, vol. 32 (1967), pp. 47–57.Google Scholar
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