ARAI, Toshiyasu

Mathematical Logic
Research interests
Proof Theory
Current research

In proof theory we are concerned with formal proofs in mathematics. I study mainly ordinal analysis. It is a field in proof theory, in which we associate ordinals with formal theories, thereby we are trying to unravel hidden structures in theories.

Selected publications
  1. Intuitionistic fixed point theories over set theories,Arch. Math Logic 54(2015), 531-553
  2. Lifting proof theory to the countable ordinals: Zermelo-Fraenkel set theory,Jour. Symb. Logic 79(2014), 325-354
  3. Proof theory of weak compactness, Jour. Math. Logic 13(2013), 1350003
  4. Proof theories of ordinals I: recursively Mahlo ordinals, Ann. Pure Appl. Logic 122(2003), 1-85
  5. Ordinal diagrams for recursively Mahlo universes, Arch. Math. Logic 39(2000), 353-391

Memberships, activities and


The Mathematical Society of Japan

Association for Symbolic Logic

Japan Association for Philosophy of Science

MSJ Autumn Prize(2003)