School of Mathematics

Prof Michael Rathjen

Professor of Pure Mathematics
Pure Mathematics

Contact details

Room: Satellite 10.29
Tel: +44 (0)113 3435109
Email: M.Rathjen @ leeds.ac.uk

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

Useful links

Personal web page

Postgraduate students

Cong Chen (2010)
Jacob Cook (2011)
Eman Dihoum (2012)
Matthew Hendtlass (2009)
Mayra Montalvo Ballesteros (2009)
Alec Thomson (2012)
Michael Toppel (2012)
Pedro Valencia Vizcaino (2009)
Albert Ziegler (2010)

Selected publications

M. Rathjen: "The realm of ordinal analysis", in: S.B. Cooper and J.K. Truss (eds.), Sets and Proofs (Cambridge University Press, 1999) 219--279.

M. Rathjen: "The disjunction and related properties for constructive Zermelo-Fraenkel set theory", Journal of Symbolic Logic 70 (2005) 1233-1254.

G. Leigh, M. Rathjen: "An ordinal analysis for theories of self-referential truth", Archive for Mathematical Logic 49 (2010) 213-247.

M. Rathjen, A. Weiermann: "Reverse Mathematics and Well-ordering Principles",in: S. Cooper, A. Sorbi (eds.): Computability in Context: Computation and Logic in the Real World} (Imperial College Press, 2011) 351-370.