An invitation to model-theoretic Galois theory

Abstract

We carry out some of Galois' 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 F ≤ K ≤ L. This exposition of a special case of [10] has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorphisms.