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We prove: Theorem 0.1Let K be a universal class. If K is categorical in cardinals of arbitrarily high cofinality, then K is categorical on a tail of cardinals.The proof stems from ideas of Adi Jarden and Will Boney, and also relies on a deep result of Shelah. As opposed to previous works, the argument is in ZFC and does not use the assumption of categoricity in a successor cardinal. The argument generalizes...
We prove that a universal class categorical in a high-enough cardinal is categorical on a tail of cardinals. As opposed to other results in the literature, we work in ZFC, do not require the categoricity cardinal to be a successor, do not assume amalgamation, and do not use large cardinals. Moreover we give an explicit bound on the “high-enough” threshold:Theorem 0.1 Let $$\psi $$ ψ be a...
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