Author/Authors :
BALDWIN, J. University of Illinois at Chicago - Department of Mathematics, Statistics, and Computer Science, USA , HYTTINEN, T. University of Helsinki - Department of Mathematics and Statistics, Finland , KESÄLÄ, M. University of Helsinki - Department of Mathematics and statistics, Finland
Abstract :
We study the history and recent developments in nonelementary model theory focusing on the framework of abstract elementary classes. We discuss the role of syntax and semantics and the motivation to generalize first order model theory to nonelementary frameworks and illuminate the study with concrete examples of classes of models. This first part introduces the main conceps and philosophies and discusses two research questions, namely categoricity transfer and the stability classification.
