Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 121 / 1 / i / e

U. A witness in the smaller model that $x$ is a countable set remains a function in the larger model, so countability is described by an upward absolute formula. It is not downward absolute: the larger model may have a new enumeration of $x$ that is absent from the smaller model, as explained by upward absoluteness of countability.