Club-guessing, stationary reflection, and coloring theorems

Abstract We obtain very strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. In particular, the simplest of our results establishes that if μ is singular and μ + → [ μ + ] μ + 2 , then there is a regular cardinal θ μ such that any fewer than cf ( μ ) stationary subsets of S ≥ θ μ + must reflect simultaneously.

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