Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 51, Issue 3 (1986), 701-708.
Supercompact Cardinals, Trees of Normal Ultrafilters, and the Partition Property
Suppose $\kappa$ is a supercompact cardinal. It is known that for every $\lambda \geq \kappa$, many normal ultrafilters on $P_\kappa(\lambda)$ have the partition property. It is also known that certain large cardinal assumptions imply the existence of normal ultrafilters without the partition property. In , we introduced the tree $T$ of normal ultrafilters associated with $\kappa$. We investigate the distribution throughout $T$ of normal ultrafilters with and normal ultrafilters without the partition property.
J. Symbolic Logic, Volume 51, Issue 3 (1986), 701-708.
First available in Project Euclid: 6 July 2007
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Barbanel, Julius B. Supercompact Cardinals, Trees of Normal Ultrafilters, and the Partition Property. J. Symbolic Logic 51 (1986), no. 3, 701--708. https://projecteuclid.org/euclid.jsl/1183742165