International Methods of Logic in Mathematics Research Group

摘要：奖项：dms -0432603首席研究员：Andreas R. Blass， Edward grifffora一系列三年一次的会议将汇集美国，俄罗斯和其他逻辑学家和集合理论家，展示将逻辑学与其他数学领域联系起来的进展和新问题。第一次会议于2004年召开，主题是逻辑、代数和几何；第二篇论文于2005年发表，讨论了算术的可计算性和模型；2006年的主题是集论的现代影响。逻辑和集合论涉及对数学最基本概念的数学研究，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得出的结论？对数学根源附近的这些问题进行系统研究而得出的理论，可以在发展阶梯上有更大的应用，例如，可以估计代数方程系统的解的数量，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。这些会议都将在俄罗斯举行，地点是位于圣彼得堡的俄罗斯科学院Steklov数学研究所的欧拉国际数学研究所。这是国际科学与工程办公室中欧和东欧项目和数学科学部基础项目联合颁发的奖项。

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.