At a Glance
- Tasks: Explore positive logic and develop new rank analogues for mathematical theories.
- Company: Join a leading research team at UEA under Dr Jonathan Kirby.
- Benefits: Gain valuable research experience and contribute to innovative mathematical projects.
- Other info: Self-funded position with potential for external funding opportunities.
- Why this job: Make a real impact in the field of mathematical logic and model theory.
- Qualifications: 1st class BSc and 2:1 Masters in mathematics or equivalent required.
Primary Supervisor: Dr Jonathan Kirby
Research Project:
Model theory is traditionally done with “classical first-order logic”, the logic which allows unlimited use of the operators AND, OR, NOT, with the EXISTS and FOR ALL quantifiers. More recently, positive logic has emerged as a useful generalisation. For a theory in positive logic, one can specify how much you are allowed to use the NOT operator and the FOR ALL quantifier: either without restriction (to get the classical case) or much less. Positive logic is more appropriate to use directly for some applications in algebra, such as for modules, and for theories which do not admit quantifier elimination.
Theories in classical logic can be classified according to their combinatorial complexity, via a number of dividing lines which are mostly due to Shelah. Many of these dividing lines are related to the existence of a suitable rank notion on formulas or on type spaces such as Morley rank, U-rank, dp-rank. These are ordinal-valued ranks which explain the complexity of a formula or type, not as a piece of syntax but in terms of how it relates to other formulas within the context of the particular theory. For example, in vector spaces, any formula has an associated vector subspace and all these ranks will give the dimension of that subspace. These ranks are then often the most useful model-theoretic tool to apply to the theories. This PhD project will aim to develop suitable analogues of Morley rank, U-rank and dp-rank in positive theories, and will explore new applications of the results obtained.
Qualifications and Expectations:
- Students should have some knowledge of mathematical logic and preferably also model theory.
- They are advised to contact Dr Kirby directly to discuss their application.
Entry Requirements:
- 1st class BSc in mathematics
- 2:1 Masters in mathematics or equivalent in mathematics
Mode of Study: Full or Part time
Start Date: 1st October 2026
Funding:
This project is offered on a self-funded basis. It is open to applicants who are self-funded or who are in the process of securing external funding. A bench fee is payable in addition to the tuition fee, to cover the cost of specialist equipment and laboratory facilities required for the research. Applicants should contact the primary supervisor for details of the bench fee applicable to this project. If you are part of the UEA alumni community, you may be eligible for a tuition fee discount. For information on doctoral funding visit our Postgraduate Student Loans page.
PhD Studentship - Ranks and Types in Positive Logic (KIRBYJ_U27EMPSFP) in Norwich employer: University of East Anglia
At our institution, we pride ourselves on fostering a vibrant research culture that encourages innovation and collaboration. As a PhD student under the guidance of Dr Jonathan Kirby, you will have access to cutting-edge resources and a supportive academic environment that promotes personal and professional growth. Located in a dynamic university setting, we offer unique opportunities for networking and engagement with leading experts in the field of mathematical logic.
StudySmarter Expert Advice🤫
We think this is how you could land PhD Studentship - Ranks and Types in Positive Logic (KIRBYJ_U27EMPSFP) in Norwich
✨Get Your Foot in the Lab
Look for local labs or research facilities that offer trainee positions. Volunteering for a few hours can not only boost your CV but also help you make connections that will come in handy when applying for roles at places like University of East Anglia.
✨Join Biology-Specific Networks
Check out biology-related meetups or online communities. Join forums where professionals discuss current research trends and techniques—these can be goldmines for connections and job leads tailored to your interests.
✨Gain Practical Experience
Don’t underestimate the power of internships or placements, even if they’re unpaid. Gaining hands-on experience in biology can set you apart when applying for trainee positions. Apply through our website to make sure you’re first in line for opportunities.
✨Attend Career Fairs
Keep an eye out for university career fairs that focus on life sciences. These events are perfect for meeting potential employers in a relaxed setting and could lead to exciting trainee roles, so come prepared to chat about what you can bring to the table at University of East Anglia.
We think you need these skills to ace PhD Studentship - Ranks and Types in Positive Logic (KIRBYJ_U27EMPSFP) in Norwich
Some tips for your application 🫡
Show off your passion for biology!:When you're crafting your CV and cover letter, don't shy away from sharing your genuine enthusiasm for biology. Include any relevant projects, coursework, or experiences that illustrate your love for the field—especially if you’ve dabbled in lab work or field studies. This is particularly important for a trainee role; we value eagerness to learn and grow!
Highlight your teamwork skills:In biology, collaboration can be key, especially in research settings. Make sure to spotlight any experience you have working in groups, whether that’s through academic projects, lab teams, or volunteering. Showing us that you’re a great team player will really help in your application.
Tailor your application documents:Make your CV and cover letter specific to the role at University of East Anglia. Highlight your relevant coursework and skills, and align them with what they’re looking for in a trainee. If you have specific interests in certain biological fields, give them a nod! It's all about making your application feel uniquely yours and lined up with what we're after.
Bring your curiosity to the forefront:As a trainee, demonstrating curiosity and a desire to learn is vital. Use your cover letter to express what specifically excites you about this role at University of East Anglia and how you see it fitting into your career path. This will show us that you're driven and ready to dive into the biological world with enthusiasm.
How to prepare for a job interview at University of East Anglia
✨Brush Up on Your Core Biology Knowledge
We should delve into the fundamental concepts of biology. Make sure you’re comfortable discussing key areas such as genetics, microbiology, and ecology, as interviewers might throw some technical questions your way to gauge your understanding. Knowing your stuff will show your passion and preparedness!
✨Show Us Your Research Skills
Since this is a trainee role, any real-world experience you have in conducting experiments or engaging in fieldwork could be a big plus. Prepare to talk about any projects or coursework, maybe even bring along a portfolio showcasing relevant lab work you’ve done. Being able to demonstrate your practical skills will help set you apart!
✨Express Your Willingness to Learn
As a trainee, they’ll likely look for your motivation and potential. Be ready to discuss what excites you about the biology field and any specific areas you’re eager to explore further. This mindset not only shows enthusiasm but also a commitment to growth!
✨Anticipate Collaborative Scenarios
Biology often involves teamwork, especially in research settings. You might face behavioural interview questions about working in a team or handling conflict. Think of examples from your studies or group projects where you successfully collaborated or resolved issues. This will demonstrate your ability to work harmoniously with others!
