Professor Michael Rathjen

Research interests

1) PROOF THEORY: Cut elimination for infinitary proof systems; ordinal analysis of classical and intuitionistic theories; witness extraction from proofs. In Proof Theory, from the work of Gentzen in the 1930's up to the present time, a central theme is the assignment of `proof theoretic ordinals' to theories, measuring their `consistency strength' and `computational power', and providing a scale against which those theories may be compared and classified.

2) INTUITIONISM and CONSTRUCTIVE MATHEMATICS: frameworks for constructivism (constructive set theory, explicit mathematics, Martin-Löf type theory); realizability and forcing techniques

3) SET THEORY (mostly non-classical): proof theory and ordinal analysis of set theories; admissible set theory; constructive and intuitionistic set theory; set theory with anti-foundation axiom; 'large cardinals' axioms in constructive and intuitionistic set theories.

4) REVERSE MATHEMATICS and COMBINATORIAL PRINCIPLES: Kruskal's Theorem, Graph Minor Theorem, ...

5) PHILOSOPHY of MATHEMATICS

Research groups and institutes

  • Pure Mathematics
<h4>Postgraduate research opportunities</h4> <p>We welcome enquiries from motivated and qualified applicants from all around the world who are interested in PhD study. Our <a href="https://physicalsciences.leeds.ac.uk/research-opportunities">research opportunities</a> allow you to search for projects and scholarships.</p>