Mathematical Sciences: Proof-Theoretical Investigations of Theories

数学科学：理论的证明理论研究

• 批准号: 9203443
• 负责人: Michael Rathjen
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1994-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203443&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Proof; Theoretical; Investigations

Rathjen intends to work on the following four problems and related issues. (1) Give an ordinal analysis of Pi-1-2 comprehension. (2) Develop strong ordinal representation systems on the basis of recursively large ordinals in lieu of their large cardinal analogues. (3) Determine the proof-theoretic strength of restricted foundations in weak set theories. (4) Is Feferman's theory T-0 together with least fixed point axioms for monotone operators conservative over T-0 with respect to arithmetic sentences? Proof theory concerns itself with axiomatic systems and methods of proof within them, particularly with the relative strength of different systems. The system A is said to be properly stronger than the system B if every proposition that has a proof in B also has a proof in A but the converse is not so. The investigator is pursuing a number of questions along these lines, varying in technical difficulty and degree of interest to the experts, but none is really susceptible to a brief discussion in laymen's terms.

Rathjen打算研究以下四个问题， 相关问题。 (1)给出Pi-1-2的序分析 理解力 (2)开发强大的序数表示系统 在递归大序数的基础上， 基数类似物 (3)确定的证明理论强度 弱集理论中的限制基础 (4)是费弗曼的 理论T-0与单调最小不动点公理 T-0上算术保守算子 句子？ 证明理论关注的是公理系统， 在他们内部的证明方法，特别是与相对 不同系统的优势。 系统A被认为是适当的 比系统B强，如果每个命题都有一个证明， B在A中也有一个证明，但匡威则不然。 的 调查人员正沿着这些线索沿着寻找一些问题， 不同的技术难度和程度的兴趣， 专家，但没有一个是真正容易受到简短的讨论， 外行的术语