Past exam of the analytic topology and axiomatic set theory course of the University of Oxford / 2009 / B / 6 / i

Let $U_1\subseteq U_2$ be transitive classes, both interpreted with actual membership. A formula $\varphi (\bar{x})$ is upward absolute from $U_1$ to $U_2$ if for every tuple of parameters $\bar{a}$ from $U_1$,For proper classes this means the usual relativization of the fixed formula's quantifiers. Full absoluteness requires the implication in both directions. The qualification on parameters matters: the smaller class must contain every object named in the comparison.