I read the beginning of chapter 1 of Wiles paper on Modular elliptic curves and Fermat's Last Theorem. There it says:
Let $p$ be an odd prime. Let $\Sigma$ be a finite set of primes including $p$ and let $\mathbb Q_\Sigma$ be the maximal extension of $\mathbb Q$ unramified outside this set and $\infty$.
As I saw in this question that there are infinitely many number fields that ramify in $p$ only. So what is meant here? I guess the key is $\infty$ since I don't know precicly what it means to ramify at $\infty$.