International Methods of Logic in Mathematics Research Group

点击翻译按钮获取中文摘要

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.