More Results on Regular Ultrafilters in ZFC

TL;DR

This paper presents new ZFC-based results on the properties of regular ultrafilters, explores related open problems, and discusses applications to topology and extended logic systems.

Contribution

It provides novel ZFC proofs regarding ultrafilter regularity and decomposability, expanding understanding without additional set-theoretic assumptions.

Findings

New ZFC results on ultrafilter regularity

List of open problems in ultrafilter theory

Applications to topology and extended logics

Abstract

We prove, in ZFC alone, some new results on regularity and decomposability of ultrafilters. We also list some problems, and furnish applications to topological spaces and to extended logics.