### Nonreflecting stationary sets in ${\mathcal P}_\kappa\lambda$

by Shelah and Shioya. [ShSy:764]

Advances in Math, 2006

Let kappa be a regular uncountable cardinal and lambda >=
kappa^+ . The principle of stationary reflection for P_kappa
lambda has been successful in settling problems of
infinite combinatorics in the case kappa = omega_1 . For a greater
kappa the principle is known to fail at some lambda . This note
shows that it fails at every lambda if kappa is the successor
of a regular uncountable cardinal or kappa is countably closed.

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