COOPERATIVE RESEARCH OF MATHEMATICAL LOGIC AND ITS RELATED FIELDS

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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.