Let's define the $V$-rank (also can be named as *set* \ *true* - rank) of a set $X$ as the minimal $\alpha$ such that $X \in V_{\alpha+1}$.

On the other hand, define the $L$-rank (also can be named as *constructible*-rank) of a constructible set $X$ as the minimal $\alpha$ such that $X \in L_{\alpha+1}$.

A set in $L$ is concordant if and only if its $V$ and $L$ ranks are equal. Formally: $$ \operatorname {conc}(X) \iff \rho^L(X)=\rho^V(X)$$

We know that $L$ does contain sets that are not concordant, an example is the diagonal of a constructible bijection between $L_\omega$ and $L_{\omega+1}$.

Now, I want to motivate the criterion of Quine's stratification in relation to this notion of concordance. So, the working assumption is that if we weaken the definition of $L$ to stratified-constructible sets (i.e., require an additional condition in defining stages of $L$, that of the defining formulas being also stratified), then the resulting hierarchy (call it stratified-$L$) can have all of its elements being concordant! That is, stratification can prevent constructible jumps.

Is there a clear counter-example to the above assumption?

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