# Who should be credited for the definition of rank in the von Neumann universe

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.

• You asked and deleted this question a while ago. Oct 11 '20 at 0:38
• The question has been changed (completely). Oct 11 '20 at 15:41

The modern definition of rank appears to have arisen gradually. The introduction of Christine Knoche's $$1973$$ masters thesis 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.