Model theory of holomorphic Functions in an o-minimal setting

UoM administered thesis: Phd

  • Authors:
  • Javier Antonio Utreras Alarcon

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.

Details

Original languageEnglish
Awarding Institution
Supervisors/Advisors
  • Alex Wilkie (Supervisor)
  • Marcus Tressl (Supervisor)
Award date1 Aug 2015