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

How do you formalise \(\varphi \colon x\)? You can define it if you fix a \(\varphi\), but in the definition of \(\theta_{\alpha}\), you quantified \(\varphi\). Therefore you need to formaise it through Goedel correspondence. Then how doy you do it?