Aspects of nonelementary stability theory

Thesis

This thesis aims to contribute to neostability and in particular to the stability theory of nonelementary classes. The central themes of the thesis are quasiminimality and excellence. We explore both classical and geometric aspects of stability theory for such classes. In particular our methods aim to utilise the topology on the space of types in these settings.

Chapter 1 is introductory and sets the necessary background on nonelementary classes. In Chapter 2 we use infinitary methods to study quasiminimal excellent classes. We give a simplified proof of the Categoricity Theorem. In Chapter 3 we study quasiminimality from the first order perspective. We look for conditions on a first order theory that allow us to build quasiminimal models with various additional properties. In Chapter 4 we look at excellent groups. We aim to generalise various results from (geometric) stability theory to this nonelementary setting.

Authors: Haykazyan, L

• DOI: 10.5287/ora-9rxe15dzo
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford