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 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