Exact saturation in simple and NIP theories

by Kaplan and Shelah and Simon. [KpShSi:1074]

A theory T is said to have exact saturation at a singular cardinal kappa if it has a kappa-saturated model which is not kappa^+-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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