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8:18 PM
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Q: "Clubbiness" of $\Pi^1_n$ sets

Noah SchweberI'm sure this is just my google-fu failing me, but: what are sufficient large cardinal axioms to guarantee "Every (boldface) $\Pi^1_n$ set of countable ordinals contains or is disjoint from a club subset of $\omega_1$"? EDIT: To clarify, I'm asking about the consistency strength over ZFC. Here...

 

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