Mathematical Sciences: Recursion Theory

数学科学：递归理论

• 批准号: 9100114
• 负责人: Steffen Lempp
• 金额: $ 9.49万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9100114&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Recursion; Theory

Lempp will pursue research in classical recursion theory. He plans to concentrate on the question of which structures can be embedded into subclasses of the Turing degrees (in particular the recursively enumerable degrees, intervals thereof, and the degrees of differences of recursively enumerable sets) in order to study the algebraic structure of these subclasses as well as the decidability of fragments of their first-order theories. Furthermore, he envisions a new framework for priority arguments similar to the forcing framework in set theory. Finally, he plans to study splittings of recursively enumerable sets. Recursion theory deals with the theoretical limits of computability. It has had a profound effect on how mathematicians think about the notion of proof as well as other concepts at the core of mathematics.

伦普将继续研究经典递归理论。 他计划集中研究哪些结构可以嵌入到图灵度的子类中（特别是递归可枚举度、其间隔以及递归可枚举集的差异度），以研究这些子类的代数结构以及他们的一阶理论片段的可判定性。 此外，他设想了一个新的优先级论证框架，类似于集合论中的强制框架。 最后，他计划研究递归可枚举集的分裂。 递归理论涉及可计算性的理论限制。 它对数学家如何思考证明概念以及数学核心的其他概念产生了深远的影响。