User blog comment:DontDrinkH20/Some ZFC-Definable very big LCOs - uncomputable?/@comment-35470197-20180830044905/@comment-35470197-20180830064424

You are talking about \(\varphi^{V_{\alpha}} \colon \beta\) with \(\beta \subset V_{\alpha}\), but I am talking about \(\varphi \colon x\).

You are not formalising \(\varphi \colon x\), but directly formalised \(\varphi^{V_{\alpha}} \colon \beta\), right? Then it is better to define \(\varphi \colon \alpha, \beta \) as \(\forall A \in \beta, \varphi^{V_{\alpha}}(A)\) and use it so that what you formalised hets clearer. At least \(\varphi \colon \beta\) does not formally make sense in ZFC.