Recursion Theory and Its Applications

递归理论及其应用

• 批准号: 1266214
• 负责人: Mingzhong Cai
• 金额: $ 9.84万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-15 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1266214&HistoricalAwards=false
• 关键词: Recursion; Theory; Its; Applications

In the proposed project, Cai plans to study classical recursion theory with emphasis on some interesting long-standing questions. In addition, he hopes to introduce new ideas and concepts to enrich the field, as well as to investigate some recent new results for different approaches and potential improvements. Cai also aims to expand the scope to applications of recursion theory, in particular he will continue the study of the degrees of provability, where proof-theoretic results can be proved using recursion-theoretic methods such as diagonalization and the recursion theorem.Recursion theory is a field of logic addressing effective content of mathematical practices (e.g., which of the mathematical procedures can be performed by automated machines, or computers). It has classical applications explaining why some mathematical problems (e.g., Hilbert's Tenth Problem) are theoretically unsolvable. The proposed project aims to improve the understanding of recursion theory by investigating old and new open problems, as well as to expand it by building connections to other fields such as proof theory. The proposed project has potential applications explaining how certain arithmetical facts could be theoretically unprovable.

在拟议的项目中，CAI计划研究古典递归理论，重点是一些有趣的长期问题。此外，他希望介绍新的想法和概念以丰富该领域，并研究一些最近的新方法和潜在改进的新结果。 CAI还旨在扩大递归理论应用的范围，特别是他将继续研究可预订的程度，在这种情况下，可以使用递归理论方法（例如对角度化和递归理论）进行证明理论结果证明结果。RECURS.RECURS.RECURS.RECURSION是通过MACHEMATIC实践的逻辑来解决的（例如，在数学上的有效内容）（例如计算机）。它具有经典的应用，解释了为什么一些数学问题（例如，希尔伯特的第十个问题）在理论上是无法解决的。拟议的项目旨在通过调查新旧开放问题以及通过与其他领域（例如证明理论）建立联系来扩大对递归理论的理解。拟议的项目具有潜在的应用，解释了某些算术事实在理论上是无法证实的。