I am writing a brief introduction to the Proper Forcing Axiom and I need a reference for Jech's notion of stationary set in $[\lambda]^\omega$ : https://en.wikipedia.org/wiki/Stationary_set#Jech's_notion
I have only been able to find a paper where Jech defined a similar concept for the family $\mathcal{P}_\kappa (\lambda) $ https://www.sciencedirect.com/science/article/pii/0003484373900144 , but I am not sure that I see how the two concepts are equivalent. To complicate things even further, Shelah defines a proper forcing in his book $\textit{Proper and Improper Forcing}$ as one that preserves stationarity in $\mathcal{P}_{\aleph_1} ( \lambda )$ rather than $[\lambda]^\omega$ as most other references do.