Phd Ranks In Positive Logic Kirbyj2U26Emp

At University of East Anglia, Norwich, applications for the Apr 2027 intake are open until Jan 31, 2027.

Where traditional model theory relies on the rigid operators of classical first-order logic, this PhD project ventures into the more nuanced territory of positive logic. By investigating how to restrict the use of NOT operators and FOR ALL quantifiers, you will explore a generalisation that is increasingly vital for algebraic applications, specifically within theories that do not readily admit quantifier elimination.

Working under the supervision of Dr. Jonathan Kirby, you will focus on the development of suitable analogues for established rank notions—such as Morley rank, U-rank, and dp-rank—within positive theories. While these ordinal-valued ranks are well-understood in classical contexts as tools for measuring combinatorial complexity, they remain largely unexplored in the positive realm. Your research will involve:

• Developing robust frameworks for rank notions in positive logic.
• Bridging the gap between Shelah-style classification and positive theory applications.
• Exploring how these ranks function as diagnostic tools for formula complexity, analogous to dimension in vector spaces.

This project is ideal for a mathematician with a strong foundation in mathematical logic and model theory who is eager to push the boundaries of current model-theoretic tools. You will be contributing to a burgeoning area of research, building upon existing foundational work on dividing lines between positive theories to create new, applicable results in the field.

University of East Anglia, Norwich is a university in the United Kingdom, founded in 1963, with 2820 international students among its 16872 total students.

The university has 400 programs, covering various subjects and research areas, allowing students to explore their interests.

Norwich provides a great location for students, with a rich history and cultural events to enjoy outside of campus.