On the $\kappa$-cub game on $\lambda$ and $I[\lambda ]$

Abstract.

We discuss the relationships between the notions of $\kappa$-cub game on $\lambda$, $\kappa$-cub subset of $\lambda$, the ideal of good subsets of $\lambda$ and the problem of adding a $\kappa$-cub into a given $\kappa$-stationary subset of $\lambda$. We also give a short introduction to the ideal of good subsets of $\lambda$.