Model Theory for Beginners. 15 Lectures

<p>This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability classification of complete types elementary extensions categoricity automorphisms and saturation; all illustrated with examples that require neither advanced alegbra nor set theory. A full proof of the compactness theorem for countable languages and its applications are given followed by a discussion of the Ehrefeucht-Mostowski technique for constructing models admitting automorphisms. Additional topics include recursive saturation nonstandard models of arithmetic Abraham Robinson's model-theoretic proof of Tarski's theorem on undefinability of truth and the proof of the Infinite Ramsey Theorem using an elementary extension of the standard model of arithmetic.</p>