Computability Theory and Its Applications

可计算性理论及其应用

• 批准号: 0901169
• 负责人: Denis Hirschfeldt
• 金额: $ 29.1万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901169&HistoricalAwards=false
• 关键词: Computability; Theory; Its; Applications

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). In this project, Antonio Montalban studies problems in both pure and applied Computability Theory. The problems in pure computability theory are part of the ongoing program to understand the structure of the Turing Degrees. As for applied computability theory, Montalban applies methods from computability theory to study the effective content and proof-theoretical strength of various areas of both classical mathematics and foundations of mathematics. He concentrates in problems related to linear orderings, Boolean algebras, and ordinals, but not exclusively. Computability Theory is the area of Logic that studies the notion of algorithm. Its applications are based on the idea that problems that can be solved using algorithms are simpler than the ones that cannot. This is used in various ways to measure the complexity of mathematical objects, constructions and proofs. It is usually the case that this analysis gives a better understanding of the subject under study.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。在这个项目中，Antonio Montalban研究了纯可计算性理论和应用可计算性理论中的问题。纯可计算性理论中的问题是理解图灵度结构的持续计划的一部分。在应用可计算性理论方面，蒙塔尔班运用可计算性理论的方法研究了古典数学和数学基础各个领域的有效内容和证明理论的强度。他集中在有关问题的线性排序，布尔代数，和序数，但不完全。 可计算性理论是研究算法概念的逻辑领域。它的应用是基于这样一种想法，即可以使用算法解决的问题比不能解决的问题更简单。它以各种方式用于衡量数学对象，构造和证明的复杂性。通常情况下，这种分析可以更好地理解所研究的主题。