Cofinal types of ultrafilters over measurable cardinals

TL;DR

This paper explores the structure of ultrafilters over measurable cardinals, extending classical results from countable to uncountable contexts and revealing new strengthened properties and models.

Contribution

It introduces a comprehensive theory of cofinal types of ultrafilters over measurable cardinals and connects it to Galvin's property, generalizing and strengthening existing results.

Findings

Established new relationships between cofinal types and Galvin's property.

Generalized key results from countable to uncountable ultrafilters.

Constructed models with diverse cofinal type structures.

Abstract

We develop the theory of cofinal types of ultrafilters over measurable cardinals and establish its connections to Galvin's property. We generalize fundamental results from the countable to the uncountable, but often in surprisingly strengthened forms, and present models with varying structures of the cofinal types of ultrafilters over measurable cardinals.