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In page 93 of Kunen's book, exercise 55 says:

Show that the following version of $\diamondsuit$ is inconsistent: There are $A_\alpha \subset \alpha$ for $\alpha < \omega_1$, such that for all stationary $A\subset \omega_1$, $\exists \alpha \in A (A \cap \alpha=A_\alpha)$.

I know that there is a version of this principle taking closed unbounded sets, but why we can't use stationary sets? Why is this version of Jensen's principle $\diamondsuit$ inconsistent?

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    Let's leave the [tag:combinatorics] tag until the [meta thread](http://meta.math.stackexchange.com/q/10435) reaches a consensus.2013-07-28

3 Answers 3