The global ${\Sigma }_{n+1}^1$-Uniformization Property and $\mathsf{BPFA}$

Abstract

We show that given a reflecting cardinal, one can produce a model of $\mathsf{BPFA}$ where the ${\Sigma }_n^1$-uniformization property holds simultaneously for all $n\ge 2$.

References in corpus (4)

• The Consistency of the ${\mathbf{\Sigma }}_3^1$-Separation Property
• Forcing Axioms and the Definabilty of the Nonstationary Ideal on ${\omega }_1$
• Forcing Axioms, the Uniformization and the Basis Property
• Forcing the ${\Pi }_3^1$-Reduction Property and a Failure of ${\Pi }_3^1$-Uniformization