Es sei ein Alphabet einer Sprache erster Stufe gegeben. Dann definiert man für Ausdrücke ${\displaystyle {}\alpha \in L^{S}}$ den Rang ${\displaystyle {}\rho }$ von ${\displaystyle {}\alpha }$ durch

1. ${\displaystyle {}\rho (\alpha )=0}$, falls ${\displaystyle {}\alpha }$ atomar ist.
2. ${\displaystyle {}\rho (\alpha )=\rho (\beta )+1}$, falls ${\displaystyle {}\alpha =\neg (\beta )}$ ist.
3. ${\displaystyle {}\rho (\alpha )=\rho (\beta )+\rho (\gamma )+1}$, falls ${\displaystyle {}\alpha =(\beta )\circ (\gamma )}$ mit ${\displaystyle {}\circ =\wedge ,\,\vee ,\,\rightarrow ,\leftrightarrow }$ ist.
4. ${\displaystyle {}\rho (\alpha )=\rho (\beta )+1}$, falls ${\displaystyle {}\alpha =\exists x\beta }$ oder ${\displaystyle {}\alpha =\forall x\beta }$ ist.