Shelah Ultrafilters
Emmanuel Balderas, David Chodounsk\'y, Osvaldo Guzm\'an

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Fuzzy and Soft Set Theory
