Definable sets from categories: exploring approaches to model theory (KIRBYU18SF) at University of East Anglia on FindAPhD.com

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Dr J Kirby No more applications being accepted Self-Funded PhD Students Only

About the Project

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.

For more information on the supervisor for this project, please go here: https://www.uea.ac.uk/mathematics/people/profile/jonathan-kirby
Type of programme: PhD
Start date of project: October 2018
Mode of study: Full time

Funding Notes

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.

Acceptable first degree: Mathematics
The standard minimum entry requirement is 2:1.

References

i) Jonathan Kirby, On quasiminimal excellent classes, J. Symbolic Logic 75 (2010), no. 2, 551–564.
ii) Anand Pillay, Geometric Stability Theory, OUP, 1996
iii) Martin Bays, Bradd Hart, Tapani Hyttinen, Meeri Kesala, and Jonathan Kirby, Quasiminimal structures and excellence, Bull. Lond. Math. Soc. 46 (2014), no. 1, 155–163.
iv) Michael Lieberman, Jirí Rosický, Classification theory for accessible categories, arXiv:1404.2528

Where will I study?

University of East Anglia

We’re one of the UK’s leading research institutions, ranked 10th in the UK for the quality of our research outputs and with more than 1,500 research students.

Definable sets from categories: exploring approaches to model theory (KIRBYU18SF)

University of East Anglia School of Mathematics