Model theory of holomorphic Functions in an o-minimal setting

  • Javier Antonio Utreras Alarcon

Student thesis: Phd


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.
Date of Award1 Aug 2015
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorAlex Wilkie (Supervisor) & Marcus Tressl (Supervisor)


  • model theory
  • complex analysis

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