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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