In the von Neumann universe (cumulative hierarchy), the rank function $R(x)$ is defined as the least ordinal $\alpha$ that $x\in V_{\alpha +1}$ (or equivalently $x\subset V_{\alpha}$). I'd like to know who gave this definition and when.
I believe that this rank should not be credited to Mirimanoff because in his 1917 paper, Mirimanoff only gave a vague idea of rank and there was no von Neumann universe at that time.
I heard that the von Neumann universe was first presented in 1930 by Zermelo. However, I have not read his paper and am not sure if Zermelo gave this definition of rank.