TITLE: Size of stationary sets
QUESTION [7 upvotes]: What can we say about the size of stationary subsets of $P_{\kappa}(\lambda)$ for infinite cardinals $\kappa, \lambda,$ especially when $\kappa=\aleph_1.$
Please give me some references, if there are any.

REPLY [6 votes]: Shelah proved using his pcf theory that the least cardinality of a stationary subset of $P_\kappa(\lambda)$ is equal to the least cardinality of a cofinal subset of $P_\kappa(\lambda)$. 
See here: M. Shioya: A proof of Shelah's strong covering theorem for $P_\kappa(\lambda)$, Asian J. Math, 12(2008), 83-98.