## Journal of Symbolic Logic

### Supercompact Cardinals, Trees of Normal Ultrafilters, and the Partition Property

Julius B. Barbanel

#### Abstract

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 [1], 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.

#### Article information

Source
J. Symbolic Logic, Volume 51, Issue 3 (1986), 701-708.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183742165

Mathematical Reviews number (MathSciNet)
MR853849

Zentralblatt MATH identifier
0623.03051

JSTOR