Document Type: Other
University of Illinois at Chicago
Department of Mathematics and Statistics University of Helsinki
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.