International Methods of Logic in Mathematics Research Group

国际数学逻辑方法研究组

• 批准号: 0432603
• 负责人: Andreas Blass
• 金额: $ 5.86万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0432603&HistoricalAwards=false
• 关键词: International; Methods; Logic; Mathematics; Research

AbstractAward: DMS-0432603Principal Investigator: Andreas R. Blass, Edward GrifforA series of three yearly meetings will bring together U.S.,Russian, and other logicians and set theorists to presentprogress and new problems connecting logic to several other areasof mathematics. The first meeting, in 2004, concerns Logic,Algebra and Geometry; the second, in 2005, addressesComputability and Models of Arithmetic; and the 2006 session willbe on The Modern Impact of Set Theory.Logic and set theory concern mathematical investigations of themost fundamental notions of mathematics, such as: What are therules of inference? What are the objects to which we apply them?How does changing this axiomatic background alter the resultingconclusions? Theories that result from systematic investigationof these concerns near the roots of mathematics can haveapplications much farther up the developmental ladder, forexample by providing estimates of the number of solutions to asystem of algebraic equations or by developing a notion ofcomplexity that can show that different dynamical systems aresimilar or genuinely distinct. Each of these meetings will beheld in Russia, at the Euler International Mathematical Instituteof the Steklov Mathematical Institute of the Russian Academy ofSciences in St. Petersburg. This is a joint award of the Officeof International Science and Engineering's Central and EasternEurope Program and the Division of Mathematical Sciences programin Foundations.

摘要奖：DMS-0432603主要研究人员：安德烈亚斯·R·布拉斯，爱德华·格里夫斯一系列三年一度的会议将汇集美国、俄罗斯和其他逻辑学家，并让理论家展示将逻辑与其他几个数学领域联系起来的进展和新问题。2004年的第一次会议涉及逻辑、代数和几何；2005年的第二次会议讨论算术的可计算性和模型；2006年的会议将讨论集合论的现代影响。逻辑和集合论涉及对数学中最基本的概念的数学调查，例如：什么是推理规则？我们应用它们的对象是什么？改变这个公理背景如何改变结果的结论？通过对这些问题进行系统研究而产生的理论可以在更高的发展阶梯上得到应用，例如，通过估计一个代数方程组的解的数量，或者通过发展一种复杂性的概念来表明不同的动力系统是相似的或真正不同的。每一次会议都将在俄罗斯圣彼得堡的俄罗斯科学院斯特克洛夫数学研究所欧拉国际数学研究所举行。这是国际科学与工程办公室的中欧和东欧计划和基金会数学科学计划部门的联合奖项。