Analytic Zariski structures and the Hrushovski construction
A set of axioms is presented defining an ‘analytic Zariski structure’, as a generalisation of Hrushovski and Zilber’s Zariski structures. Some consequences of the axioms are explored. A simple example of a structure constructed using Hrushovski’s method of free amalgamation is shown to be a non-triv...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2005
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| Subjects: |
| _version_ | 1797090384271114240 |
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| author | Peatfield, N Zilber, B |
| author_facet | Peatfield, N Zilber, B |
| author_sort | Peatfield, N |
| collection | OXFORD |
| description | A set of axioms is presented defining an ‘analytic Zariski structure’, as a generalisation of Hrushovski and Zilber’s Zariski structures. Some consequences of the axioms are explored. A simple example of a structure constructed using Hrushovski’s method of free amalgamation is shown to be a non-trivial example of an analytic Zariski structure. A number of ‘quasi-analytic’ results are derived for this example e.g. analogues of Chow’s theorem and the proper mapping theorem. |
| first_indexed | 2024-03-07T03:17:48Z |
| format | Journal article |
| id | oxford-uuid:b665dbb2-537b-4f9e-bed9-8588969a01f2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:17:48Z |
| publishDate | 2005 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:b665dbb2-537b-4f9e-bed9-8588969a01f22022-03-27T04:40:39ZAnalytic Zariski structures and the Hrushovski constructionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b665dbb2-537b-4f9e-bed9-8588969a01f2MathematicsEnglishOxford University Research Archive - ValetElsevier2005Peatfield, NZilber, BA set of axioms is presented defining an ‘analytic Zariski structure’, as a generalisation of Hrushovski and Zilber’s Zariski structures. Some consequences of the axioms are explored. A simple example of a structure constructed using Hrushovski’s method of free amalgamation is shown to be a non-trivial example of an analytic Zariski structure. A number of ‘quasi-analytic’ results are derived for this example e.g. analogues of Chow’s theorem and the proper mapping theorem. |
| spellingShingle | Mathematics Peatfield, N Zilber, B Analytic Zariski structures and the Hrushovski construction |
| title | Analytic Zariski structures and the Hrushovski construction |
| title_full | Analytic Zariski structures and the Hrushovski construction |
| title_fullStr | Analytic Zariski structures and the Hrushovski construction |
| title_full_unstemmed | Analytic Zariski structures and the Hrushovski construction |
| title_short | Analytic Zariski structures and the Hrushovski construction |
| title_sort | analytic zariski structures and the hrushovski construction |
| topic | Mathematics |
| work_keys_str_mv | AT peatfieldn analyticzariskistructuresandthehrushovskiconstruction AT zilberb analyticzariskistructuresandthehrushovskiconstruction |