Model theory of expansions of fields with analytic functions
Lead Research Organisation:
University of Leeds
Department Name: Pure Mathematics
Abstract
Model theory, a branch of mathematical logic, provides powerful tools to classify mathematical structures according to the complexity of their definable sets. This has generated striking applications in various fields, from real analytic geometry to number theory.
This project will study the model theoretic properties of expansions of fields related to several analytic functions of interest in mathematics, but whose behaviour is not yet captured by current model theory, with the aim of obtaining model theoretic control that has potential for new applications.
Possible directions include:
- classify contraction groups of transexponential functions
- prove model-completeness results for suitable reducts of complex exponentiation
- prove cases of exponential-algebraic closure for abelian exponentials
- explore connections between surreal numbers, transseries and model theoretic classes of non-oscillating functions
This project will study the model theoretic properties of expansions of fields related to several analytic functions of interest in mathematics, but whose behaviour is not yet captured by current model theory, with the aim of obtaining model theoretic control that has potential for new applications.
Possible directions include:
- classify contraction groups of transexponential functions
- prove model-completeness results for suitable reducts of complex exponentiation
- prove cases of exponential-algebraic closure for abelian exponentials
- explore connections between surreal numbers, transseries and model theoretic classes of non-oscillating functions
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/R513258/1 | 01/10/2018 | 30/09/2023 | |||
| 2273512 | Studentship | EP/R513258/1 | 01/10/2019 | 31/03/2023 | Ibrahim Mohammed |