Beyond First Order Logic: From number of structures to structure of numbers: Part I

Abstract

We study the history and recent developments in nonelementary<br />model theory focusing on the framework of abstract<br />elementary classes. We discuss the role of syntax and semantics<br />and the motivation to generalize first order model theory to nonelementary<br />frameworks and illuminate the study with concrete examples<br />of classes of models. <br /><br />This first part introduces the main conceps and philosophies and<br />discusses two research questions, namely categoricity transfer and<br />the stability classification.