Again http://www.cs.elte.hu/~kope/ss3.pdf .
After the Remark 2, I have some problem to prove that there exists a increasing decomposition of $\delta<\lambda^+$ ($\delta$ ordinal ? or cardinal ?) as $\delta=\bigcup_{i<\kappa}A_i^\delta$ with $|A_i^\delta|<\lambda$. I've tried to distinguish according to the position of $\delta$ regard to $cf(\lambda)$ and $\lambda$ etc... Another question : do we implicitly suppose that $\lambda$ is a cardinal ? because, $\lambda^+$ is defined to be the first cardinal greater than the ordinal $\lambda$ ... ?
Could somebody give me an indication ? Thanks.