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Supercompact cardinals, trees of normal ultrafilters, and the partition property1
Published online by Cambridge University Press: 12 March 2014
Abstract
Suppose κ is a supercompact cardinal. It is known that for every λ ≥ κ, many normal ultrafilters on Pκ(λ) have the partition property. It is also known that certain large cardinal assumptions imply the existence of normal ultrafilters without the partition property. In [1], we introduced the tree T of normal ultrafilters associated with κ. We investigate the distribution throughout T of normal ultrafilters with and normal ultrafilters without the partition property.
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- Copyright © Association for Symbolic Logic 1986
Footnotes
I would like to thank the referee for useful suggestions on a previous version of this paper.