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.

在数学逻辑的特殊一年，佛罗里达大学，2006- 2007在数学逻辑的特殊一年将致力于探索各种渠道之间的沟通几个领域的逻辑以及其余的数学科学。 在其中一个工作坊中，我们将集中讨论可计算性、有效描述集合论和可计算分析与数值方法和分析之间的关系，例如实数和真实的函数的有效闭集和有效性的研究。潜在的专题将包括算法随机性、量子计算、逆向数学。 第二个研讨会将可定义强迫和确定性的当前趋势与测量理论、势理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。 第三个工作坊将进一步探讨奇异红雀和晚餐模型之间的联系。 最近在大基数和内部模型方面的工作有助于推进集合论的前沿及其在数学中的应用。特别的一年将汇集来自数理逻辑许多领域的顶尖科学家，努力推进我们对这一基本学科的理解。 正如数学是科学的语言并提供科学的基础一样，逻辑也是数学的语言并提供数学的基础。逻辑学的学科起源于古典哲学，今天在许多学科中都有分支，包括数学和哲学，以及计算机科学、语言学和法律。 专家系统中使用的一种逻辑推理机，例如，它可以帮助医生借助计算机诊断疾病。目前对混合算法的研究是在软件开发中使用逻辑来绘制飞机的真实的飞行计划。虽然该计划是基于数学系，其他部门，包括哲学和计算机科学，也将参与。该项目更广泛的影响包括强调研究生、初级研究人员和女数学家的参与。也将重点关注来自东南地区的参与者。 我们将出版在特别会议期间提出的工作的会议记录。