Professor Michael Rathjen
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