One Repeat Point Gives a Closed, Unbounded Ultrafilter on {\omega_1}

TL;DR

This paper establishes that the consistency of having a closed unbounded ultrafilter on omega_1 as an ultrafilter is equivalent to ZFC with one measurable cardinal, linking set-theoretic ultrafilter properties to large cardinal assumptions.

Contribution

It proves that the existence of a closed unbounded ultrafilter on omega_1 as an ultrafilter has the same consistency strength as ZFC with one measurable cardinal.

Findings

The consistency strength of the ultrafilter condition equals ZFC plus one measurable cardinal.

The paper demonstrates the equivalence between ultrafilter existence and large cardinal assumptions.

Provides a precise set-theoretic characterization of ultrafilter properties on omega_1.

Abstract

It is shown that the consistency strength of ZF + DC + "the closed unbounded ultrafilter on omega_1 is an ultrafilter" is exactly ZFC + one measurable cardinal.