what is the explicit definition of $K_\lambda$-filters?

Question

I have a doubt with the definition of a concept: $K_\lambda$-filters.

We say that a filter $\mathcal{F}\subseteq\mathcal{P}(\omega)$ is a $K_\lambda$- filter if it is $\textbf{generated}$ by less than $\lambda$ compact subset of $\mathcal{P}(\omega)$.

In that definition which is the meaning of "generated" if each compact set in $\mathcal{P}(\omega)$ can't be an element of $\mathcal{F}$?

Thanks for advance.

Answer 1

The union of the compact sets generates the filter. This is what is meant.