Definable sets from categories: exploring approaches to model theory (KIRBY_U18SF)
Model theory is a branch of mathematical logic which considers the category of all models of a given theory. One feature of the models is that they can always be built up from small models by a process called amalgamation. This is due to the downward Lowenheim-Skolem theorem. Another approach to models due to Fraisse is to start with a category of small models (usually finite) and consider what models you can build out of them, instead of starting with a theory. Accessible categories are a different approach to the same idea which are more general, but recent work of Lieberman, Boney, Rosicky and others has shown that the two subjects have much to offer each other.
This PhD project will explore these two approaches to model theory. Specifically, you will investigate to what extent the definable sets of a mathematical structure can be recovered from the category of models of the theory of the structure. There are many related questions, and potential applications to various areas of mathematics.
Applicants should have some knowledge of category theory and at least one of mathematical logic, model theory and algebraic geometry. An interest in the philosophy of mathematics would be an advantage, but it is not necessary. The PhD project can be tailored to suit the applicant, and applicants are encouraged to contact Dr Kirby directly to discuss their application.
This PhD project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found at http://www.uea.ac.uk/study/postgraduate/research-degrees/fees-and-funding.
A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. The amount charged annually will vary considerably depending on the nature of the project and applicants should contact the primary supervisor for further information about the fee associated with the project.
This job comes from a partnership with Science Magazine and