Let $L$ be any language for predicate logic and $S$ be any set of sentences in $L$. Prove that $S$ is satisfiable iff it has an infinite model.
So I know that a set of sentences is only satisfiable if every finite subset is also satisfiable. I don't know where to go from there though, because I don't think I can apply Skolem-L$\ddot{o}$wenheim Theorem, since the set isn't necessarily countable?