In the Von Neumann cumulative hierarchy, $V:=\bigcup_\alpha(V_\alpha)$ is called the universe. Is there a name for the individual levels $V_\alpha$?
Just as one can say "The closure of $A$ is defined as $$cl(A):={...}"$$
I would like to be able to say "The _______ of $\alpha$ is defined as $$V_\alpha:={...}"$$