Phd Around The Hod Dichotomy Asperodu26Emp

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

Mathematicians who thrive in the deep abstractions of set theory and foundational logic will find a rigorous intellectual home in this research programme. Candidates will engage directly with the HOD (hereditarily definable from ordinals) dichotomy, a cornerstone of contemporary set theory that examines the relationship between the class of sets definable from ordinals and the broader universe of ZFC.

Researching Woodin’s HOD Conjecture

Working under the supervision of Dr. David Asperó, the successful candidate will explore the tension between HOD being close to the real universe versus significantly smaller, a debate central to Woodin’s ultimate-L programme. You will move beyond standard set-theoretic frameworks to investigate:

• Prospects for falsifying the HOD Conjecture.
• Complex patterns of ω-strongly measurable cardinals within HOD.
• The application of choiceless large cardinals and advanced forcing techniques over ZFC models.

This PhD is designed for those who aim to contribute to the foundational debates defining the limits and structure of mathematical universes, requiring a high level of comfort with abstract modeling and proof-based inquiry.

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.