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Mathematical Logic

Research Project

Project/Area Number 61302010
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionScience University of Tokyo (1987-1988)
Kyushu University (1986)

Principal Investigator

UESU Tadahiro  Science University of Tokyo ・ Professor, 理学部, 教授 (60015550)

Co-Investigator(Kenkyū-buntansha) SHIRAI Kohio  Shizuoka University ・ Assistant Professor, 理学部, 助教授 (70077915)
UMEZAWA Toshio  Shizuoka University ・ Professor, 理学部, 教授 (40021919)
EDA Katsuya  Tsukuba University ・ Assistant Professor, 数学系, 助教授 (90015826)
MOTOHASHI Nobuyoshi  Tsukuba University ・ Professor, 数学系, 教授 (70015874)
NISHIMURA Toshio  Tsukuba University ・ Professor, 数学系, 教授 (00015471)
八杉 満利子  京都産業大学, 理学部, 教授 (90022277)
難波 完爾  東京大学, 教養学部, 教授 (40015524)
Project Period (FY) 1986 – 1988
Project Status Completed (Fiscal Year 1988)
Budget Amount *help
¥9,300,000 (Direct Cost: ¥9,300,000)
Fiscal Year 1988: ¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 1987: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1986: ¥3,100,000 (Direct Cost: ¥3,100,000)
KeywordsMathematical Logic / Foundation of Mathematics / Proof Thevy / Set Thevy / Model Thevy / Construction Mathematics / Recursin Thery / 超準解析 / 数学史 / 超準解析数学史
Research Abstract

We organized five working groups. the groups exchanged informations each other, and opened meetings on several occasions. In those meetings, researchers discussed and announced results of their researches.
In the followings, we list up the main results of the groups. Group I(Proof theory): The relations between subsystems of arithmetic with weak inductive definitions and ordinals were explained. Several results concerned with refrection pronciples and Paris-Harrington principles were obtained. Generalized built-up systems of fundamental sequences were proposed.
Group II(Set theory and model theory): A set theory with modality and a set theory with intensionality were proposed. Assuming existence of several large cardinals, interesting abelian groups were constructed. Several properties of -stable rings were explained.
Group III(Constructive mathematics): A theory of Fuzzy computability was made up. A consistency proof of Beeson's system PRS was given. A two-storied theory of transfinite mechanisms was proposed.
Group IV(Theory of logical structures): It was shown that modal operators are interpretable by quantifiers in intermediate predlcate logics. The relation between the syntax and the semantics of logics without a part of structural rules, -calculus, and categorical grammars were uniformly discussed.
Group V(Theory of non-standard universes): In a nonfinitary logic, an interpretation of infinitesimal caculus was obtained. Several properties of iterated polynomials in nonstandard analysis were explained. For Hilbert irreducibility theorem, a condition for that Z-If is finite was given, and it was shown that the bound is given by a polynomial. A nonstandard set theory, in which there are models of the five nonstandard set theories NST, IST, NSTE, NS2 and *NST, respectively, was proposed.

Report

(4 results)
  • 1988 Annual Research Report   Final Research Report Summary
  • 1987 Annual Research Report
  • 1986 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] 本橋信義: Journal of Symbolic Logic. 51. 1022-1028 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 江田勝哉: Israel Journal of Mathematics. 60. 22-30 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 梅沢敏郎: Reports of Fuculty of Science,Shizuoka University. 23. 1-7 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 八杉満利子: Tsukuba Jourmal of Mathematics. 12. 97-114 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 小野寛晰: Studia Logica. 47. (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 田中尚夫: "選択公理と数学" 遊星社, 238 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Nobuyoshi, Motohashi.: "Preservation Theven and Relativization Theven for Cofinal Extensions" Journal of Symbolic Logic. 51. 1022-1028 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Katzuya Eda.: "A Characterization of ^1-free Abelian groups and its Application to the Chase Radical" Israel Journal of Mathematics. 60. 22-30 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Toshio Umezawa.: "Prenex normal form of xA( ) B" Reports of Fuculty of Science, shizuoka University. 23. 1-7 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Mariko Yasugi.: "A two-Storied Universe of Transfinite Mechanisms" Tsukuba Journal of Mathematics. 12. 97-114 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Reijiro Kurata: "Extensios of Friedman - McAloon - Simpson Priciple and Refrectin Priciple of ATRO"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hisao Tanaka: Axcim of Choice in Mathematics. Yusei Sya, 238 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 梅沢敏郎: Repoto of Facalty of Sieme,Shignkka University. 23. 1-7 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] 小野寛晰: Stndia Logica. 47. (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 小野寛晰: Proc of Heyting '88 Conference.

    • Related Report
      1988 Annual Research Report
  • [Publications] 田中尚夫: "選択公理と数学" 遊星社, 1-238 (1987)

    • Related Report
      1988 Annual Research Report
  • [Publications] 江田勝哉: Tsukuba Journal of Mathematics. 11. 353-360 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] 小野寛晰: Zeitschrift fur Mathematische logik und Grundlagen der Mathematik. 33. 317-333 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] 小野寛晰: Reports on Mathematical Logic. 21.

    • Related Report
      1987 Annual Research Report
  • [Publications] 倉田令二朗: Proceedings of Beijing Symposium(Third Asian Conference of Mathematial Logic).

    • Related Report
      1987 Annual Research Report
  • [Publications] 八杉満利子: Tsukuba Journal of Mathematics. 12. (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] 八杉満利子: Tsukuba Journal of Mathematics. 12. (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] 田中尚夫: "選択公理と数学" 遊星社, 240 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] Nobuyoshi Motohashi: The Journal of Symbolic Logic. 51. 1022-1028 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] Mariko Yasugi: Commentarii Mathematici Universitatis Sancti Pauli. 35. 247-257 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] Hiroakira Ono: Studia Logica. 45. 19-33 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] Hiroakira Ono: Zeitschrift f【u!¨】r Mathematische Logik und Grundlagen der Mathematik.

    • Related Report
      1986 Annual Research Report

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Published: 1987-03-31   Modified: 2016-04-21  

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