Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727839 |
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Title: | Model theory of holomorphic functions in an o-minimal setting | ||||||
Author: | Utreras Alarcon, Javier Antonio |
ISNI:
0000 0004 6495 1067
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Awarding Body: | University of Manchester | ||||||
Current Institution: | University of Manchester | ||||||
Date of Award: | 2015 | ||||||
Availability of Full Text: |
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Abstract: | |||||||
Given an o-minimal structure on the real field, we consider an elementary extension to a non-archimedean field R, and interpret the algebraically closed field K=R[sqrt(-1)] on this extension. We construct two pregeometries on K: one by considering images under C-definable holomorphic functions, and the other by considering images under proper restrictions of C-definable holomorphic functions together with algebraic functions (i.e. zeros of polynomials).We show that these two pregeometries are the same, generalising a result of A. Wilkie for complex holomorphic functions. We also do some work towards generalising another result of his on local definability of complex holomorphic functions to our non-archimedean setting.
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Supervisor: | Not available | Sponsor: | Not available | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.727839 | DOI: | Not available | ||||
Keywords: | model theory ; complex analysis | ||||||
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