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

<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>

Research groups and institutes

• Pure Mathematics
• Logic

Current postgraduate researchers

• Richard Matthews
• Shuangshuang Shu
• Shuwei Wang

<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://phd.leeds.ac.uk">research opportunities</a> allow you to search for projects and scholarships.</p>

Projects

<li><a href="//phd.leeds.ac.uk/project/1203-ordinal-analysis-of-theories">Ordinal Analysis of Theories</a></li>