Classification theory for abstract elementary classes

Μ-abstract Elementary Classes and Other Generalizations

We introduce μ-Abstract Elementary Classes (μ-AECs) as a broad framework for model theory that includes complete boolean algebras and metric spaces, and begin to develop their classification theory. Moreover, we note that μ-AECs correspond precisely to accessible categories in which all morphisms are monomorphisms, and begin the process of reconciling these divergent perspectives: for example, ...

Categoricity and Stability in Abstract Elementary Classes

Categoricity and Stability in Abstract Elementary Classes byMonica M. VanDieren This thesis tackles the classification theory of non-elementary classes from twoperspectives. In Chapter II we work towards a categoricity transfer theorem, whileChapter III focuses on the development of a stability theory for abstract elementaryclasses (AECs).The results in Chapter II are in a c...

Beyond first order logic: From number of structures to structure of numbers: Part II

We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This second part continues to study the question of catecoricitytrans...

Advances In Classification Theory For Abstract Elementary Classes

A Survey on Tame Abstract Elementary Classes

Tame abstract elementary classes are a broad nonelementary framework for model theory that encompasses several examples of interest. In recent years, progress toward developing a classification theory for them has been made. Abstract independence relations such as Shelah’s good frames have been found to be key objects. Several new categoricity transfers have been obtained. We survey these devel...