This is an exercise that Serre's paper How to use Finite Fields for Problems Concerning Infinite Fields.
Let $L$ be an infinite set of prime numbers. For every $p \in L$ let $k(p)$ denote a denumerable field of characteristic $p$. Let $A = \prod k(p)$ be the product of the $k(p)$'s. Show that there exists a quotient of $A$ which is isomorphic to a subfield of $\mathbf{C}$. (Hint: Use an ultrafilter on $L$.)
How do you prove this? I've just started learning about ultrafilters and ultraproducts, so I don't see yet why the hint provided is a good hint. Maybe I've yet to make some realization about ultrafilters, or yet to see the right important theorem to see how to prove this.
Is this exercise just part of the model-theoretic Lefschetz Principal? The part that says "a first-order statement in the language or rings is true in all but finitely many algebraically closed fields of characteristic $p$ if it's true in $\mathbf{C}$" part?