User blog comment:DontDrinkH20/Some ZFC-Definable very big LCOs - uncomputable?/@comment-35470197-20180830044905/@comment-36540075-20180830161407

Regardless of the way to formalize \(\theta_\alpha\), the same function will always result. As long as it is able to quantify over all FOST formulae bounded in \(V_\alpha\) (for example using colored trees, which I guess is the method of formalization).