Definition:Ordinal Exponentiation

Definition
Let $x$ and $y$ be ordinals. $x^y$ is defined using Transfinite Recursion:


 * $\displaystyle x^\varnothing = 1$
 * $\displaystyle x^{z^+} = ( x^z \cdot x )$
 * $\displaystyle x^y = \bigcup_{z \in y} x^z$ for limit ordinals $y$