SM: Logic Year at the University of Florida

SM：佛罗里达大学逻辑年

• 批准号: 0532644
• 负责人: Jindrich Zapletal
• 金额: $ 13.8万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0532644&HistoricalAwards=false
• 关键词: SM; Logic; Year; University; Florida

Special Year in Mathematical Logic, University of Florida, 2006-2007The special year in mathematical logic will be devoted to theexploration of various channels of communication between severalfields of logic as well as the rest of the mathematical sciences.Mathematical logic is entering a phase of increasingly intenseconversation with other parts of mathematics. In one workshop, wewill concentrate on the relationship between computability, effectivedescriptive set theory and computable analysis on one hand andnumerical methods and analysis on the other, such as the study ofeffectively closed sets and effectivity of reals and real functions.Potential special topics will include algorithmic randomness, quantumcomputation, reverse mathematics. The second workshop will relate thecurrent trends in definable forcing and determinacy with measuretheory, potential theory and dynamical systems, as well as with thegames used in biomathematics or economics. Special topics includeBorel equivalence relations and definable forcing. The third workshopwill further explore the connections between singular cardinals andinner models. Recent work on large cardinals and inner models hashelped to advance the frontier of set theory and its applications tomathematics.The special year will bring together leading scientists from manyareas of mathematical logic, in an effort to advance our understandingof this fundamental discipline. Just as mathematics is the languageof science and provides the foundation of science, so logic is thelanguage of mathematics and provides the foundation of mathematics.The subject of logic has its roots in classical philosophy and todayhas branches in many disciplines, including mathematics andphilosophy, as well as computer science, linguistics, and law. Logicis used in expert systems which, for example, help doctors diagnoseillness with the aid of computers. Current research on hybridalgorithms is using logic in the development of software which willmap out the flight plan of an airplane in real time. While the programis based in the mathematics department, other departments, includingphilosophy and computer science, will also participate. The broaderimpact of the project includes an emphasis on participation ofgraduate students, junior researchers and women mathematicians. Therewill also be a focus on participants from the Southeast region. Wewill publish proceedings of the work presented during the specialyear.

佛罗里达大学数理逻辑特别年，2006-2007数理逻辑特别年将致力于探索逻辑的几个领域以及数学科学的其他领域之间的各种沟通渠道。数理逻辑正在进入一个日益发展的阶段。与数学其他部分的激烈对话。 在一次研讨会上，我们将一方面集中于可计算性、有效描述集合论和可计算分析之间的关系，另一方面集中于数值方法和分析之间的关系，例如有效闭集的研究以及实数和实函数的有效性。潜在的专题将包括算法随机性、量子计算、逆向数学。 第二次研讨会将把可定义的强迫和确定性的当前趋势与测度论、势论和动力系统以及生物数学或经济学中使用的游戏联系起来。 专题包括 Borel 等价关系和可定义的强迫。 第三次研讨会将进一步探讨奇异基数与内部模型之间的联系。 最近关于大基数和内部模型的工作有助于推进集合论及其在数学中的应用的前沿。特殊的一年将汇集来自数理逻辑许多领域的领先科学家，以增进我们对这一基础学科的理解。 正如数学是科学的语言并为科学提供了基础一样，逻辑是数学的语言并为数学提供了基础。逻辑学科起源于古典哲学，如今在许多学科中都有分支，包括数学和哲学。如计算机科学、语言学和法律。 逻辑用于专家系统，例如，帮助医生借助计算机诊断疾病。目前对混合算法的研究正在使用逻辑来开发软件，该软件将实时绘制飞机的飞行计划。虽然该计划以数学系为基础，但包括哲学和计算机科学在内的其他系也将参与。该项目更广泛的影响包括强调研究生、初级研究人员和女性数学家的参与。来自东南地区的参与者也将受到关注。 我们将出版这一特殊年份中所呈现的作品集。