A note on the combinatorial principles $\diamondsuit (E)$
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- by Keith J. Devlin PDF
- Proc. Amer. Math. Soc. 72 (1978), 163-165 Request permission
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.References
- Keith J. Devlin, Variations on $\diamondsuit$, J. Symbolic Logic 44 (1979), no. 1, 51–58. MR 523488, DOI 10.2307/2273703 —, Iterated Souslin forcing, the principles $\diamondsuit (E)$, and a generalisation of the Axiom SAD, Israel J. Math. (to appear).
- Saharon Shelah, Whitehead groups may be not free, even assuming CH. I, Israel J. Math. 28 (1977), no. 3, 193–204. MR 469757, DOI 10.1007/BF02759809
Additional Information
- © Copyright 1978 American Mathematical Society
- 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