Shelah’s eventual categoricity conjecture in universal classes,
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We present Sebastien Vasey’s proof of Shelah’s categoricity conjecture in universal classes. First we change the substructure relation of the given class to obtain an AEC with better properties, except that the union axiom might not hold. To prove that the union axiom holds, we use the independence framework AxFr developed by Shelah, build an “independent” tree assuming the failure of union, and contradict stability.