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We give a complete and elementary proof of the following upward categoricity theorem: let K be a local abstract elementary class with amalgamation and joint embedding, arbitrarily large models, and countable Löwenheim–Skolem number. If K is categorical in ℵ1 then K is categorical in every uncountable cardinal. In particular, this provides a new proof of the upward part of Morley’s theorem in first...
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