International Methods of Logic in Mathematics Research Group

摘要奖：DMS-0432603主要研究者：Andreas R.布拉斯，爱德华格里菲斯一系列的三个年度会议将汇集美国，俄罗斯，和其他逻辑学家和集理论家提出的进展和新的问题连接逻辑到其他几个领域的数学。 第一次会议，在2004年，涉及逻辑，代数和几何;第二次会议，在2005年，解决可计算性和模型的算术;和2006年的会议将在现代的影响集Theory.Logic和集theory关注的数学调查themost基本概念的数学，如：什么是therules的推理？我们将它们应用于哪些对象？如何改变这一公理化的背景改变所产生的结论？ 从系统地研究这些数学根源附近的问题中产生的理论可以在更高的发展阶梯上得到应用，例如通过提供代数方程组的解的数量的估计，或者通过发展一种复杂性的概念，可以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举行，地点是位于彼得堡的俄罗斯科学院斯捷克洛夫数学研究所欧拉国际数学研究所。 这是国际科学与工程部中欧和东欧项目和数学科学部基金会项目的联合奖项。

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.