Separating properties for normal ultrafilters

TL;DR

This paper introduces separating properties for normal ultrafilters, demonstrating how certain large cardinal properties can be distinguished and used to identify unique ultrafilters without measurable cardinals.

Contribution

It establishes that compactness and supercompactness are separable properties, while compactness and measurability are not, and shows how to use these properties to find distinct ultrafilters.

Findings

Compactness and supercompactness are separable properties.

Compactness and measurability are not separable.

Method to produce distinct ultrafilters excluding measurables.

Abstract

We define separating properties for normal ultrafilters. We prove that compactness and supercompactness are separable, yet compactness and measurability are not. We describe how to use separating properties in order to elicit distinct normal ultrafilters which do not contain the measurables.