Say that a formula $\phi$ defines a set $x$ from parameters $a_1, \dots, a_n$ if $\phi(a_1, \dots, a_n, x)$ holds (in $V$) but for $y \neq x$ $\phi(a_1, \dots, a_n, y)$ does not hold.
Is it true that: If $x$ is definable from ordinal parameters, then it is definable from ordinal parameters by a $\Sigma_2$ formula.
Note that in In the model $L$, everything is definable by ordinal parameters.
Any set definable from ordinal parameters is definable from a slightly different set of ordinal parameters by a $\Sigma_2$ formula; this is a consequence of the reflection theorem, which - given a definition $\varphi$ of $x$ with ordinal parameters $\gamma_1,...,\gamma_n$ - states that there is an ordinal $\alpha$ such that $x,\gamma_1,...,\gamma_n\in V_\alpha$ and $$V_\alpha\models\forall z(\varphi(\gamma_1,...,\gamma_n,z)\iff z=x).$$ We can now define $x$ from the parameters $\gamma_1,...,\gamma_n,\alpha$ via the above condition; saying "$V_\alpha\models ...$" is $\Sigma_2$ (in fact, $\Sigma_1$) in $V$: saying that an appropriate Skolem function exists is an $\exists$ ranging over $V$ on top of a bunch of quantifiers bounded by $V_\alpha$.