SM: Logic Year at the University of Florida

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各个领域以及其他数学科学之间的各种交流渠道。数理逻辑正进入与数学其他部分日益密集的借阅阶段。在一个工作坊中，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，例如有效闭集的研究、实函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、逆数学。第二个工作坊将用测量理论、位势理论和动力系统，以及生物数学或经济学中使用的游戏，联系可定义的强迫和确定性的当前趋势。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索奇数基数和内部模型之间的联系。最近关于大型基数和内部模型的工作帮助推进了集合论及其在数学中的应用的前沿。特别年将聚集来自数理逻辑许多领域的顶尖科学家，努力促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、语言学和法学。逻辑学用于专家系统，例如，帮助医生在计算机的帮助下诊断疾病。目前对混合算法的研究是在软件开发中使用逻辑，该软件将实时绘制飞机的飞行计划。虽然该项目设在数学系，但包括哲学和计算机科学在内的其他系也将参与其中。该项目的广泛影响包括强调研究生、初级研究人员和女性数学家的参与。会议还将重点关注来自东南部地区的与会者。我们将公布在专题会议期间提出的工作的记录。

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.