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2010 Fiscal Year Self-evaluation Report

Proof-theoretic investigations on set theories

Research Project

  • PDF
Project/Area Number 20340020
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionChiba University (2009-2012)
Kobe University (2008)

Principal Investigator

ARAI Toshiyasu  Chiba University, 大学院・理学研究科, 教授 (40193049)

Project Period (FY) 2008 – 2012
Keywords数学基礎論
Research Abstract

従来の帰納的巨大順序数の公理系の帰納的順序数による証明論的研究に含まれる技法と構成方法を精査し、それらが当該の帰納的巨大順序数がそれの帰納的類似物たる巨大基数の証明論的解析に転用できることを、スコーレム関数を証明図の解析と順序数の表示の双方に導入することで示していく。これは、対象とする巨大基数が大きくなればなるほど技術的に困難になるであろうが、帰納的巨大順序数の公理系の帰納的順序数による証明論的研究における経験から考えて乗り越えることができない障壁ではない。更に、構成可能性公理V=L と矛盾する巨大基数(例:可測基数)へと研究対象を広げていく。

  • Research Products

    (12 results)

All 2011 2010 2009 2008 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (5 results) Book (1 results) Remarks (1 results)

  • [Journal Article] Wellfoundedness proofs by means of non-monotonic inductive definitions II : first order operators2010

    • Author(s)
      Toshiyasu Arai
    • Journal Title

      Annals of Pure and Applied Logic vol.162

      Pages: 107-143

    • Peer Reviewed
  • [Journal Article] Intuitionistic fixed point theories over Heyting arithmetic2010

    • Author(s)
      Toshiyasu Arai
    • Journal Title

      Proofs, Categories and Computations

      Pages: 1-14

    • Peer Reviewed
  • [Journal Article] Iterating the recursively Mahlo operations2009

    • Author(s)
      Toshiyasu Arai
    • Journal Title

      Proceedings of the thirteenth International Congress of Logic Methodology, Philosophy of Science

      Pages: 21-35

    • Peer Reviewed
  • [Journal Article] Non-elementary speed-ups in logic calculi2008

    • Author(s)
      Toshiyasu Arai
    • Journal Title

      Mathematical Logic Quarterly vol.6

      Pages: 629-640

    • Peer Reviewed
  • [Journal Article] Polynomial-size Frege proofs of Bollob\'as' theorem on the trace of sets2008

    • Author(s)
      Akihiro Nozaki, Toshiyasu Arai, Noriko Honda Arai
    • Journal Title

      Prcceedings of the Japan Academy, Ser.A vol.84

      Pages: 159-161

    • Peer Reviewed
  • [Presentation] Lifting up the proof theory to the countables2011

    • Author(s)
      Toshiyasu Arai
    • Organizer
      Kobe Colloquium on Logic, Statistics and Informatics
    • Place of Presentation
      神戸大学
    • Year and Date
      2011-03-30
  • [Presentation] Wellfoundedness proofs and the bounds on provability in set theories2010

    • Author(s)
      Toshiyasu Arai
    • Organizer
      Oberseminar
    • Place of Presentation
      LMU Muenchen
    • Year and Date
      2010-09-22
  • [Presentation] Search problems in bounded arithmetics2010

    • Author(s)
      Toshiyasu Arai
    • Organizer
      A Proof Theory Workshop
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-18
  • [Presentation] In germ, Leeds Symposium on2009

    • Author(s)
      Toshiyasu Arai
    • Organizer
      Proof Theory and Constructivism
    • Place of Presentation
      University of Leeds
    • Year and Date
      2009-07-06
  • [Presentation] Provably $\Delta^{0}_{2}$ and weakly descending chains of ordinals2009

    • Author(s)
      Toshiyasu Arai
    • Organizer
      Eleventh Asian Logic Conference
    • Place of Presentation
      National University of Singapore
    • Year and Date
      2009-06-25
  • [Book] 計算とは何か2009

    • Author(s)
      新井紀子・新井敏康
    • Total Pages
      224
    • Publisher
      東京図書
  • [Remarks]

    • URL

      http://researchmap.jp/tosarai/

URL: 

Published: 2012-02-13   Modified: 2016-04-21  

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