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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| מחברים אחרים: | |
| פורמט: | Thesis |
| שפה: | English |
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2017
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| נושאים: |
| _version_ | 1826316374378545152 |
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| author | Efem, SU |
| author2 | Zilber, B |
| author_facet | Zilber, B Efem, SU |
| author_sort | Efem, SU |
| collection | OXFORD |
| description | <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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| first_indexed | 2024-03-06T21:04:47Z |
| format | Thesis |
| id | oxford-uuid:3c14ca5d-c3d7-4233-93d3-81a4e20c4d1f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:44:00Z |
| publishDate | 2017 |
| record_format | dspace |
| spelling | oxford-uuid:3c14ca5d-c3d7-4233-93d3-81a4e20c4d1f2024-12-07T15:19:02ZTheory of specialisationsThesishttp://purl.org/coar/resource_type/c_db06uuid:3c14ca5d-c3d7-4233-93d3-81a4e20c4d1fModel TheoryEnglishHyrax Deposit2017Efem, SUZilber, B<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> |
| spellingShingle | Model Theory Efem, SU Theory of specialisations |
| title | Theory of specialisations |
| title_full | Theory of specialisations |
| title_fullStr | Theory of specialisations |
| title_full_unstemmed | Theory of specialisations |
| title_short | Theory of specialisations |
| title_sort | theory of specialisations |
| topic | Model Theory |
| work_keys_str_mv | AT efemsu theoryofspecialisations |