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Destructibility of stationary subsets of Pκλ

✍ Scribed by Sakaé Fuchino; Greg Piper

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
166 KB
Volume
51
Category
Article
ISSN
0044-3050

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✦ Synopsis

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 ∈ Pκλ : 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 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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