User blog comment:P進大好きbot/ZFC-variant of Rayo's number/@comment-37485018-20190816235322/@comment-35470197-20190905221546

Since \(f\) includes occurrence of a free variable, the satisfaction \(V_{\alpha} \models f\) does not make sense. A structure which we can ask the satisfaction of \(f\) is a domain equipped with a constant term in it. In this case, since we assume \(\mathbb{N} \subset V_{\alpha}\), we have \(n \in V_{\alpha}\), and hence the structure \((V_{\alpha},n)\) makes sense.

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