Interpolation in model theory (2507.19097v1)

Abstract: We bring an abstract model theory perspective to interpolation. We ask, what is the role of interpolation in the study of extensions of first order logic, such as infinitary logics, generalized quantifiers and higher order logics? The abstract model theory approach reveals the basic connections between various interpolation properties in isolation, on their own, as well as with respect to other model theoretic properties, such as compactness.