权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Mathematical Logic

数理逻辑

基本信息

批准号：
61302010
负责人：
UESU Tadahiro
金额：
$ 5.95万
依托单位：
Science University of Tokyo (1987-1988)Kyushu University (1986)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1986
资助国家：
日本
起止时间：
1986 至 1988
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61302010/
关键词：
Mathematical 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

项目摘要

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.

我们组织了五个工作组。各小组相互交换了信息，并举行了多次会议。在这些会议上，研究人员讨论并宣布了他们的研究成果。下面，我们列出了这些小组的主要成果。第一组（证明论）：说明了具有弱归纳定义的算术子系统与序数之间的关系。得到了与反射原理和Paris-Harrington原理有关的几个结果。第二组（集合论与模型论）：提出了具有模态性的集合论和具有内涵性的集合论。假设存在多个大基数，构造了有趣的阿贝尔群。第三组（构造数学）：建立了Fuzzy可计算性理论。给出了Beeson系统PRS的一致性证明。第四组（逻辑结构理论）：证明了模态算子在中间谓词逻辑中可由量词解释。对不含结构规则的逻辑、微积分和范畴文法的语法和语义之间的关系进行了统一的讨论。第V组（非标准论）：在非有限逻辑中，得到了无穷小演算的一个解释。说明了非标准分析中迭代多项式的几个性质。对于Hilbert不可约性定理，给出了Z-If有限的条件，并证明了其界由多项式给出.提出了一种非标准集合论，其中分别有NST、IST、NSTE、NS2和 * NST五种非标准集合论的模型.