On $({\Sigma }_1^2{)}^{uB}$ Absoluteness Between V and HOD

Gabriel Goldberg, Dan Hathaway

We put together Woodin's ${\Sigma }_1^2$ basis theorem of AD${}^{+}$ and Vopěnka's theorem to conclude the following: If there is a proper class of Woodin cardinals, then every $(Σ^2_1)^{\mbox…