| Abstract: | For a regular cardinal κ with κ <κ = κ and κ ≤ λ , we construct generically (forcing by a < κ‐closed κ +‐c. c. p. o.‐set ℙ0) a subset S of {x ∈ P κ λ : x ∩ κ is a singular ordinal} such that S is stationary in a strong sense (F IAκ λ ‐stationary in our terminology) but the stationarity of S can be destroyed by a κ +‐c. c. forcing ℙ* (in V ℙ) which does not add any new element of P κ λ . Actually ℙ* can be chosen so that ℙ* is κ‐strategically closed. However we show that such ℙ* itself cannot be κ‐strategically closed or even <κ‐strategically closed if κ is inaccessible. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
