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Destructibility of stationary subsets of P κ λ
Author(s) -
Fuchino Sakaé,
Piper Greg
Publication year - 2005
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200510009
Subject(s) - forcing (mathematics) , mathematics , construct (python library) , terminology , element (criminal law) , set (abstract data type) , combinatorics , closed set , pure mathematics , mathematical analysis , computer science , philosophy , linguistics , political science , law , programming language
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 ℙ 0 ) a subset S of { x ∈ P κ λ : x ∩ κ is a singular ordinal} such that S is stationary in a strong sense ( F IA κ 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)