Shelah Ultrafilters

TL;DR

This paper introduces Shelah ultrafilters, explores their construction via forcing, and demonstrates their relation to I-ultrafilters for various Borel ideals, advancing understanding of ultrafilter properties.

Contribution

It presents the first construction method for Shelah ultrafilters using forcing and establishes their connection to I-ultrafilters for multiple Borel ideals.

Findings

Shelah ultrafilters can be added through a specific forcing notion.

Shelah ultrafilters are I-ultrafilters for many Borel ideals.

The paper expands the understanding of ultrafilter classifications.

Abstract

In this paper, we study a special type of ultrafilter which we call Shelah ultrafilter. We show that it is possible to add a Shelah ultrafilter using a special forcing notion. We also show that Shelah ultrafilters turn out to be I-ultrafilters for many Borel ideals.