Destructibility of stationary subsets of Pκλ

Mathematical Logic Quarterly 51 (6):560-569 (2005)
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Abstract

For a regular cardinal κ with κ<κ = κ and κ ≤ λ , we construct generically a subset S of {x ∈ Pκλ : x ∩ κ is a singular ordinal} such that S is stationary in a strong sense but the stationarity of S can be destroyed by a κ+-c. c. forcing ℙ* which does not add any new element of Pκλ . 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

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Approachability and games on posets.Yasuo Yoshinobu - 2003 - Journal of Symbolic Logic 68 (2):589-606.

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