Hi all,

In Kunen's book, one of the exercises is the following:

Show that for $\displaystyle \kappa > \omega$, |H($\displaystyle \kappa$)| =$\displaystyle 2^{< \kappa}$.

But, H($\displaystyle \omega$) = V($\displaystyle \omega$) and |V($\displaystyle \omega$)| = $\displaystyle \omega$. Also, $\displaystyle 2^{< \omega}= \omega$ (because $\displaystyle 2^{< \omega}$ is the cardinality of the union of omega many finite sets (the characteristic functions for each n)).

Is this wrong?

Thanks in advance!

Sam