| Project/Area Number |
04302009
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kobe University |
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Principal Investigator |
KAKUDA Yuzuru Kobe University, Professor, 工学部, 教授 (50031365)
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| Co-Investigator(Kenkyū-buntansha) |
KAMAE Tetsuro Osaka City University, Faculty of Science, 理学部, 教授 (80047258)
MOTOHASHI Nobuyoshi University, of Tsukuba School of Mathematics, 数学系, 教授 (70015874)
KAMO Sizuo University of Osaka Prefecture, College of Integrated Arts and Sciences, 総合科学部, 助教授 (30128764)
HAYASHI Susumu Ryukoku University, Faculty of Science and Technology, 理工学部, 教授 (40156443)
ONO Hiroakira Japan Advanced Institute of Science and Technology, Professor, 教授 (90055319)
篠田 寿一 名古屋大学, 大学院・人間情報学研究科, 助教授 (30022685)
田中 一之 東北大学, 理学部, 助教授 (70188291)
高橋 譲嗣 神戸大学, 発達科学部, 助教授 (30197149)
八杉 舶満利子 京都産業大学, 理学部, 教授 (90022277)
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| Project Period (FY) |
1992 – 1994
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| Project Status |
Completed (Fiscal Year 1994)
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| Budget Amount *help |
¥9,400,000 (Direct Cost: ¥9,400,000)
Fiscal Year 1994: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1993: ¥3,900,000 (Direct Cost: ¥3,900,000)
Fiscal Year 1992: ¥3,700,000 (Direct Cost: ¥3,700,000)
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| Keywords | Non-standard logic / ideal / Non-standard analysis / Linear logic / Mathematical logic / 集合論的トポロジー / 安定性理論 / クリプケモデル / substructural logic / Browerian-valued model / elementary embedding / recursive ordinal / 型理論 / ファイマン種分 / Honest Polynomial Degree / Substructural Logic / Reverse Mathemtics / Motomsthematics / New-stardird Analysis / Inner Models / Supercompect Cardinals / BCK algchra |
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| Research Abstract |
The main aim of this project is that researchers in mathematical logic, proof theory, recursion theory, set theory, model theory, non-standard analysis and theoretical computer science cooperatively research in the view point of applications of mathematical logic to those fields. During the term, the most important development was the study of non-standard logic led by Hiroakira Ono. Logic obtained by restricting several structural rules had been studied by several logicians in Japan. Hoever, under the stimulus of emergence of linear logic by Girald, the study of substructural logic has been active again by Ono and cooperators. Under these circumstances, Ono proposed the international meeting of non-standard logic and planed to open the 1st meeting in Japan. The meeting, called NSL'94, was held in Kanazawa last fall, and many important results concerning non-standard logic were announced. It is highly expected this branch will be developed more in future. The group of set theorist led by Shizuo Kamo developed the study of ideals and combinatorial properties on sets. They obtained several outstanding results in this branch. The group of model theorist led by Motohashi studied the stability theory, especially applications of the theory to the algebraic structures, and obtained several intereting results. The group of non-standard anlysis led by Teturou Kamae developed the non-standard method of functional analysis, and obtained several important results. Kakuda proposed the method of non-standard analysis without non-standard models several years ago.
Inspired by this method, Yasugi developed metamathematics of language with infinitely long formulas, and applied it to non-standard analysis.
In view of the reduction of research results to education, Kakuda is now developping the new teaching method of calculus by using the system of predicates and writing a text book of calculus.
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