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A note on a result of Kunen and Pelletier

Published online by Cambridge University Press:  12 March 2014

Julius B. Barbanel
Julius B. Barbanel*
Affiliation:
Department of Mathematics, Union College, Schenectady, New York 12308, E-mail: [email protected],[email protected]
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Abstract

Suppose that U and U′ are normal ultrafilters associated with some supercompact cardinal. How may we compare U and U′? In what ways are they similar, and in what ways are they different? Partial answers are given in [1], [2], [3], [5], [6], and [7]. In this paper, we continue this study.

In [6], Menas introduced a combinatorial principle χ(U) of normal ultrafilters U associated with supercompact cardinals, and showed that normal ultrafilters satisfying this property also satisfy a partition property. In [5], Kunen and Pelletier showed that this partition property for U does not imply χ(U). Using results from [3], we present a different method of finding such normal ultrafilters which satisfy the partition property but do not satisfy χ(U). Our method yields a large collection of such normal ultrafilters.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 2 , June 1992 , pp. 461 - 465
Copyright
Copyright © Association for Symbolic Logic 1992

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References

REFERENCES

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