Dr Richard Matthews


I completed a PhD in mathematical logic at the University of Leeds in 2021 under the supervision of Michael Rathjen and Andrew Brooke-Taylor. Before that, I was at the University of Bristol, where I completed a masters degree in Mathematics. 


I am currently a Research Associate, investigating Collection Principles in Set Theory. This is a project to separate, under set theory without Power Set, axioms such as Replacement, Collection, Reflection and the various schemes of Dependent Choices.



  • Constructing the Constructible Universe Constructively (joint with Michael Rathjen): 2022, arxiv: 2206.08283
  • ZFC without Power Set II: Reflection Strikes Back (joint with Victoria Gitman): 2022, arxiv: 2206.06220
  • Very large set axioms over constructive set theories (joint with Hanul Jeon): 2022, arXiv: 2204.05831
  • Taking Reinhardt’s Power Away: The Journal of Symbolic Logic, p 1-21, 2022. doi:10.1017/jsl.2022.9. 

Links to talks and slides:

Research interests

Set Theory, in particular:

  • Axiomatic Set Theory
  • Large Cardinal Axioms
  • Set Theory Without the Power Set
  • Intuitionistic Set Theory
  • Choiceless Set Theory
<h4>Research projects</h4> <p>Any research projects I'm currently working on will be listed below. Our list of all <a href="https://eps.leeds.ac.uk/dir/research-projects">research projects</a> allows you to view and search the full list of projects in the faculty.</p>


  • PhD, University of Leeds
  • MSci Mathematics, University of Bristol

Student education

Currently I am a supervisor for a group undergraduate project in mathematics, titled Rethinking Set Theory, as part of the module MATH3001.

Research groups and institutes

  • Pure Mathematics
  • Logic