 Solution

With the same parameter $\alpha =({\omega }_1{)}^M$, letThis formula is downward absolute: if the larger transitive model has no such function, then neither can the smaller model, since any witness in the smaller model would remain a witness in the larger one. The model $M$ satisfies ${\phi }_2(\alpha )$, while the generic surjection $\bigcup G$ makes it false in $M[G]$. Therefore it is not upward absolute.