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Explore advanced concepts in applied model theory with Silvain Rideau-Kikuchi from CNRS, Université de Paris in this lecture from the Fields Institute. Delve into introdefinable sets, residual extensions, and the principles of disjunction and contradiction. Examine the "Swiss Cheese" theorem and its interesting cases, and gain insights into stability embedded in model theory. This in-depth lecture is part of a series on applied model theory, offering a comprehensive look at cutting-edge research in the field.