Exact saturation in simple and NIP theories

A theory $T$ is said to have exact saturation at a singular cardinal $κ$ if it has a $κ$-saturated model which is not $κ^{+}$-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact saturation. Also, an NIP theory has exact saturation if and only if it is not distal. This gives a new characterization of distality.

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