Mathematical Sciences: Topics in Logic and the Foundations of Mathematics

数学科学：逻辑主题和数学基础

• 批准号: 8703242
• 负责人: Solomon Feferman
• 金额: $ 11.03万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703242&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Logic; Foundations

Several research problems and problem areas are under investigation, primarily in proof theory, with applications to constructive and semi-constructive mathematics and theoretical computer science. In addition a new problem area is proposed, relating recursion theory, logic, and algebra. The topics are as follows: 1. Recursion-theoretic analogues between algebra and logic (e.g., Higman's finite embedding theorem and Kleene's finite axiomatizability theorem). 2. Proof-theoretic reduction of subsystems of analysis to weak theories. (a) Reduction to PRA and below. (b) Reduction to PA. 3. Proof-theory of constructive theories of functions and classes. (a) The strength of the general principle of monotone inductive definition. (b) The strength of a constructive programming system. (c) Polymorphism. The interplay between mathematical logic and theoretical computer science has always been and continues to be very fruitful.

几个研究问题和问题领域是根据 调查，主要是在证明理论，与应用， 构造性和半构造性数学和理论 计算机科学 此外，还提出了一个新的问题领域， 与递归理论、逻辑和代数有关。 主题为 如下所示： 1. 代数与逻辑之间的递归论类比 (e.g., Higman有限嵌入定理和Kleene有限嵌入定理 公理化定理）。 2. 分析的子系统到弱的证明论约化 理论 (a)减少到PRA及以下。 (b)减少到PA。 3. 构造函数论的证明理论 班 (a)单调性一般原理的强度 归纳定义 (b)建设性编程系统的优势。 (c)多态 数理逻辑与理论计算机的相互作用 科学一直是，并将继续是非常富有成果的。