Forcing Axioms and the Definabilty of the Nonstationary Ideal on ${\omega }_1$

Stefan Hoffelner, Paul Larson, Ralf Schindler +1

We show that under $\BMM$ and "there exists a Woodin cardinal$"$, the nonstationary ideal on ${\omega }_1$ can not be defined by a ${\Sigma }_1$ formula with parameter $A\subset {\omega }_1$. We show tha…