Model Theory in Algebra, Analysis and Arithmetic: A Preface

Abstract

Model theory is a branch of mathematical logic dealing with mathematical structures (models) from the point of view of first order logical definability. Although comparatively young, it is now well established, its major textbooks including [6, 17, 34, 43, 53]. A typical goal of model theory is to build, study and classify mathematical universes in which some given axioms (usually expressed in a first order way) are satisfied. Thus model theory has remote roots in the birth of non-Euclidean geometries and in the effort to realize them in suitable mathematical settings where their revolutionary (non-standard) assumptions are obeyed. Some major achievements of mathematical logic in the first half of the twentieth century, such as the Godel Compactness Theorem around 1930, underpin modern model theory.