GENERIC STABILITY AND MODES OF CONVERGENCE

Abstract We expand the study of generic stability in three different directions. Generic stability is best understood as a property of types in $NIP$ theories in classical logic. In this article, we make attempts to generalize our understanding to Keisler measures instead of types, arbitrary theories instead of $NIP$ theories, and continuous logic instead of classical logic. For this purpose, we study randomization of first-order structures/theories and modes of convergence of types/measures.