A possible typo in the definition for V in a book on set theory.

Question

I am currently reading a book in set theory which defines $V$ the universe of sets thus:

(1) $V_0=\emptyset$

(2) $V_{\alpha +1} = \mathcal{P} (V_{\alpha})$

(3) If $\beta$ is a limit ordinal, then $V_\alpha = \bigcup \{V_\beta |\beta < \alpha\}$

Shouldn't that say "if $\alpha$ is a limit ordinal?"

Answer 1

Yes, it should be $\alpha$. This is clear because $\beta$ is a dummy variable. (I'm sure there's a more set theoretic term for it, but it eludes me).