Theory of specialisations

Thesis

This thesis aims to develop a theory of specialisations for Zariski structures. The main question this thesis is centred around is when is a specialisation is κ-universal?

In Chapter 3 we look at the case of algebraically closed fields and Zariski structures definable in these. We show that any specialisation of an algebraically closed field defines a residue map of a valuation ring, and moreover we show that any residue map induces a κ-universal specialisation whenever the algebraically closed field is κ-saturated over the residue field.

In Chapters 4 and 5 we look at the κ-universal specialisations of finite and infinite covers of Zariski structures. Under some natural assumptions we show that a specialisation of a cover of a Zariski structure is κ-universal if and only if it extends a κ-universal specialisation of a base Zariski structures and satisfies a simple axiom.

Authors: Efem, SU

• DOI: 10.5287/ora-8negdpwgz
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Model Theroy; Zariski structures; Specialisations; Zariski geometries; Valued fields
• Subjects: Model Theory