Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 121 / 1 / iv

For every tuple of parameters $\bar{a}\in M^n$, a downward absolute formula transfers truth from the larger structure to the smaller one:The condition concerns every parameter tuple from $M$, not merely parameter-free sentences.

For every tuple of parameters $\bar{a}\in M^n$, an upward absolute formula transfers truth from the smaller structure to the larger one:These definitions of directional set-theoretic absoluteness do not themselves require the structures to be transitive.

A formula has set-theoretic absoluteness between these structures when both directions hold for every $\bar{a}\in M^n$:Equivalently, it is both a downward absolute formula and an upward absolute formula between them.