Journal of Symbolic Logic

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

Julius B. Barbanel

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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

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183742165

Mathematical Reviews number (MathSciNet)
MR853849

Zentralblatt MATH identifier
0623.03051

JSTOR
links.jstor.org

Citation

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


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