The new notion of interpolative fusions provides a unified framework for studying many examples of "generic constructions" in model theory. Some, like structures with generic predicates, or algebraically closed fields with several independent valuations, are explicitly interpolative fusions, while others, like structures with generic automorphisms, or fields with generic operators, are bi-interpretable with interpolative fusions. The idea is to take two expansions T and T' of a common reduct theory and study models of their union such that the T and T' structures interact "randomly" up to constrains imposed by the common reduct. If T and T' are model-complete, this is equivalent to studying the model companion of the union theory. In joint work with Erik Walsberg and Minh Tran, we study two basic questions: (1) When does the interpolative fusion exist as a first-order theory, and how can we axiomatize it? (2) How can we understand properties of the interpolative fusion in terms of properties of the theories T, T', and their common reduct?
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