Richard Matthews

Richard Matthews is a Research Associate at the School of Mathematics within the Faculty of Engineering and Physical Sciences at the University of Leeds. He completed his PhD in 2021 under Professor Michael Rathjen and Dr Andrew Brooke-Taylor, focusing on foundational aspects of set theory in weakened axiomatic frameworks.

Education:

• MSci Mathematics, University of Bristol

Research Profile: Dr. Matthews specializes in advanced set theory with emphasis on large cardinal axioms in non-standard contexts. His work critically examines Zermelo-Fraenkel set theory without the power set axiom, intuitionistic set theory, and choiceless frameworks. Current investigations explore the boundaries of consistency strength in alternative set-theoretic universes.

Publication Trends: His research output centers on foundational challenges in set theory, particularly the behavior of large cardinals when standard axioms are restricted. The preprint "Taking Reinhardt's Power Away" (2020) exemplifies this focus by analyzing Reinhardt cardinals in power-set-free contexts, contributing to ongoing debates about the hierarchy of large cardinal axioms.

Academic Engagement: He actively participates in the international logic community through presentations at major seminars including CUNY Set Theory Seminar, Barcelona Set Theory Seminar, and London Mathematical Society events. His work is affiliated with the Logic research group at Leeds.