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Shelah has proved that ♢ does not imply that ♢ ( E ) (E) holds for every stationary set E ⊆ ω 1 E ⊆ {ω _1} . We prove that, in the other direction, whenever ♢ ( E ) (E) holds there are disjoint stationary sets F , G ⊆ E F,G ⊆ E such that both ♢ ( F ) (F) and ♢ ( G ) (G) hold.
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Keith Devlin (1978) studied this question.
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