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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on the combinatorial principles $ \diamondsuit (E)$


Author: Keith J. Devlin
Journal: Proc. Amer. Math. Soc. 72 (1978), 163-165
MSC: Primary 04A20
DOI: https://doi.org/10.1090/S0002-9939-1978-0491194-9
MathSciNet review: 0491194
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Abstract: Shelah has proved that $ \diamondsuit $ does not imply that $ \diamondsuit (E)$ holds for every stationary set $ E \subseteq {\omega _1}$. We prove that, in the other direction, whenever $ \diamondsuit (E)$ holds there are disjoint stationary sets $ F,G \subseteq E$ such that both $ \diamondsuit (F)$ and $ \diamondsuit (G)$ hold.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0491194-9
Keywords: $ \diamondsuit (E)$, stationary set, countably complete ideal, prime ideal
Article copyright: © Copyright 1978 American Mathematical Society