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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:727839 |
| Date | January 2015 |
| Creators | Utreras Alarcon, Javier Antonio |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/model-theory-of-holomorphic-functions-in-an-ominimal-setting(a1ff9ed8-d7dd-4c56-91ad-581eca7c7989).html |
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