An invitation to model-theoretic Galois theory

We carry out some of Galois’s work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by definably closed subsets of M, assume that T codes finite sets, and obtain the fundamental duality of Galois theory matching subgroups of the Galois group of L over F with intermediate extensions. This exposition of a special case of Poizat’s “Une th'eorie de Galois imaginaire.” (1983) has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorphisms.