A universe with no ordinal-definable, stationary, co-stationary subset of $\omega_1$

TL;DR

This paper proves that the existence of a measurable cardinal is equiconsistent with a model of ZFC where no ordinal-definable, stationary, co-stationary subset of  exists, linking large cardinals to definability properties.

Contribution

It establishes an equiconsistency result connecting large cardinal assumptions with the non-existence of certain definable subsets of .

Findings

Equiconsistency between measurable cardinals and absence of certain definable subsets of .

Shows that such definability properties are consistent with large cardinal axioms.

Provides a new perspective on the relationship between large cardinals and definability in set theory.

Abstract

It is shown that the existence of a measurable cardinal is equiconsistent to a model of ZFC in which there is no ordinal-definable, stationary, costationary subset of $\omega_1$