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This improves several classical results of Shelah.\n  $\\mathbf{Theorem}$\n  Let $\\mu \\ge \\text{LS} (K)$. If $K$ is categorical in a $\\lambda \\ge \\beth_{\\left(2^{\\mu}\\right)^+}$, then:\n  1) Whenever $M_0, M_1, M_2 \\in K_\\mu$ are such that $M_1$ and $M_2$ are limit over $M_0$, we have $M_1 \\cong_{M_0} M_2$.\n  2) If $\\mu > \\text{LS} (K)$, the model of size $\\lambda$ is ","authors_text":"Monica M. 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