Definition ($lambda$-closed). A forcing $\mathbb{P}$ is called $\lambda$-closed if any family $\{p_{\alpha }:\alpha <\gamma \}$ for $\gamma <\lambda$ that is a descending chain:

$$\alpha <\beta ⟹p_{\beta }<p_{\alpha }$$

there is $q$ such that $q\le p_{\alpha }$ for all $\alpha <\gamma$.