Theory of specialisations
<p>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?</p> <p>In Chapter 3 we look at the case of algebraically closed fields and Zariski structures definable in...
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| Fformat: | Traethawd Ymchwil |
| Iaith: | English |
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2017
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| Crynodeb: | <p>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?</p>
<p>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.</p>
<p>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.</p>
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