Toshiyasu Arai

Address: Rokkodai, Nada, Kobe 657-8501, Japan
Office: Room 415, 3rd Building for Research of Science and Technology at Rokkodai Campus of Kobe University
E-mail: arai @ kurt.scitec.kobe-u.ac.jp

Tel: 078-803-6245 (+81-78-803-6245)
Fax: 078-803-6320 (+81-78-803-6320)

publications

• T. Arai, An accessibility proof of ordinal diagrams in intuitionistic theories for iterated inductive definitions, Tsukuba Journal of Mathematics vol. 8 (1984), pp.209-218.
• T. Arai, A subsystem of classical analysis proper to Takeuti's reduction method for $\Pi^{1}_{1}$-analysis, Tsukuba Journal of Mathematics vol. 9 (1985), pp. 21-29.
• T. Arai, A consistency proof of a system including Feferman's $ID_{\xi}$ by Takeuti's reduction method, Tsukuba Journal of Mathematics vol. 11 (1987), pp. 227-239.
• T. Arai, Derivability conditions on Rosser's provability predicates, Notre Dame Journal of Formal Logic vol. 31 (1990), pp. 487-497.
• T. Arai, A slow growing analogue to Buchholz' proof, Annals of Pure and Applied Logic vol. 54 (1991), pp. 101-120.
• T. Arai, Consistency proof via pointwise induction, Archive for Mathematical Logic vol. 37 (1998), pp. 149-165. Reviewed by A. Weiermann, Bulletin of Symbolic Logic vol.8 (2002), pp. 536-537.
• T. Arai, Variations on a theme by Weiermann, Journal of Symbolic Logic vol. 63 (1998), pp. 897-925.
• T. Arai, Some results on cut-elimination, provable well-orderings, induction and reflection, Annals of Pure and Applied Logic vol. 95 (1998), pp. 93-184. Reviewed by J. Avigad, Bulletin of Symbolic Logic vol. 7 (2001), pp. 77-78.
• T. Arai, Introduction to finitary analyses of proof figures, In: Sets and Proofs. Invited papers from Logic Colloquium '97-European Meeting of the Association for Symbolic Logic, Leeds, July 1997. Ed. by S. B. Cooper and J. K. Truss, London Mathematical Society Lecture Notes, vol. 258, Cambridge University Press (1999), pp.1-25.
• T. Arai and G. Mints, Extended normal form theorems for logical proofs from axioms, Theoretical Computer Science vol. 232 (2000), pp.121-132, an invited paper from CADE-13(Conference on Automated DEduction1996).
• T. Arai, A bounded arithmetic $AID$ for Frege systems, Annals of Pure and Applied Logic vol. 103 (2000), pp. 155-199.
• T. Arai, Ordinal diagrams for recursively Mahlo universes, Archive for Mathematical Logic vol. 39 (2000), pp. 353-391.
• T. Arai, Ordinal diagrams for $\Pi_{3}$-reflection, Journal of Symbolic Logic vol. 65 (2000), pp.1375-1394. Reviewed by A. Setzer, to appear in Bulletin of Symbolic Logic.
• T. Arai, On the slowly well orderedness of $\varepsilon_{0}$, Mathematical Logic Quarterly vol. 48 (2002), pp. 125-130.
• T. Arai, Epsilon substitution method for theories of jump hierarchies, Archive for Mathematical Logic vol. 41 (2002), pp. 123-153.
• T. Arai, Epsilon substitution method for $ID_{1}(\Pi^{0}_{1}\lor\Sigma_{1}^{0})$, Annals of Pure and Applied Logic vol. 121 (2003), pp. 163-208.
• T. Arai, Proof theory for theories of ordinals I:recursively Mahlo ordinals, Annals of Pure and Applied Logic vol. 122 (2003), pp. 1-85.
• T. Arai, Proof theory for theories of ordinals II:$\Pi_{3}$-Reflection,
• T. Arai, Wellfoundedness proofs by means of non-monotonic inductive definitions I: $\Pi^{0}_{2}$-operators, Journal of Symbolic Logic vol. 69 (2004), pp. 830-850.

course notes

• Introduction to Proof Theory
• Introduction to Ordinal Analyses