In the von Neumann universe (also known as the cumulative hierarchy), the rank $R(x)$ 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.



Who should be credited for the definition of rank in the von Neumann universe
The modern definition of rank appears to have arisen gradually. The introduction of [Christine Knoche's $1973$ masters thesis](https://preserve.lehigh.edu/cgi/viewcontent.cgi?article=5189&context=etd) gives a good summary: it seems to have begun with Mirimanoff in $1917$ and been given its modern form by Tarski in $1955$. Along the way von Neumann, Russell, and Bernays (and others) played with it in various ways.


I think it would ultimately be an oversimplification to try to credit it to any individual author - nor is there any particular need to.


