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Title: Theory of specialisations
Author: Efem, Sukru Ugur
ISNI:       0000 0004 9356 1527
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2017
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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.
Supervisor: Zilber, Boris Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Model Theory