Update (1/15): See slides here.
I will be contributing a session at the 2018 ASL Winter Meeting at the Joint Mathematics Meetings on Saturday, January 13. This talk is based on a recent paper of mine which can be found on the arxiv here.
Abstract: Simpson used arithmetic forcing to show that every countable model has an undefinable, inductive subset such that the expansion is pointwise definable. Enayat later showed that there are many models with the property that every expansion upon adding a predicate for an undefinable class is pointwise definable. We refer to models with this property as Enayat models. That is, a model is Enayat if for each undefinable class , the expansion is pointwise definable. In this talk we show that a model is Enayat if it is countable, has no proper cofinal submodels and is a conservative extension of each of its elementary cuts.