A note on iterating strongly $(<\hat{I}»)$-closed stationary $\hat{I}{»}^{+}$-cc forcing

Abstract

We give an exposition of an iteration theorem for iterating $(<\hat{I}»)$-closed stationary $\hat{I}{»}^{+}$-cc forcing with supports of size $<\hat{I}»$ and preserving these two properties. We discuss the relation of this theorem with other iteration theorems and forcing axioms that have appeared in the literature, notably the one from \cite{Sh80}.