U.S.-U.K. Collaborative Research: Exponentiation and O-Minimal Expansions of R

9224546 Marker这个为期三年的美英合作数学研究奖获得者分别是伊利诺伊大学芝加哥校区和厄巴纳-香槟校区的David E.Marker、C.Ward Henson和Lou van den Dries，以及牛津大学数学研究所的Angus Macintyre、Alex Wilkie和Kobi Peterzil。这项研究的目的是将复杂的分析方法应用于R的指数和O-极小展开的模型理论中。模型理论结果如此公平地表明，R的可定义指数的子集在许多方面表现得像半代数子集和次解析子集。研究人员将研究R的更精细的可定义性和增长率问题，并将他们的结果扩展到自然扩展，从而允许进一步的分析结构。这一合作利用了牛津大学和伊利诺伊大学研究小组的互补专业知识。两人都在模型理论和分析界面、指数运算和以指数项定义的复杂函数的研究方面进行了广泛的工作。由于指数定义的半代数集和次解析集在许多数学和工程领域中自然而然地出现，本研究将促进人们对它们在实代数和实解析几何、动力系统、控制论、统计学和机器人学中的应用的理解。***

9224546 Marker This three-year award for U.S.-United Kingdom cooperative research in mathematics involves David E. Marker, C. Ward Henson, Lou van den Dries of the Chicago and Urbana-Champaign campuses of the University of Illinois respectively, and Angus Macintyre, Alex Wilkie, Kobi Peterzil of Oxford University's Mathematics Institute. The objectives of the research is to apply complex analytical methods to model theory in exponentiation and O- minimal expansions of R. Model theoretical results obtained so fair show that subsets of R definable exponentiation behave in many ways like semialgebraic and subanalytic subsets. The investigators will study finer definability and growth rate questions of R and extend their results to natural expansions allowing further analytical structure. This collaboration takes advantage of the complementary expertise of the Oxford and University of Illinois research groups. Both have worked extensively on model theory and analysis interface, exponentiation, and study of complex function defined in exponential terms. Since exponentially defined semialgebraic and subanalytic sets arise naturally in many mathematical and engineering fields, this research will advance understanding of their uses in real algebraic and real analytic geometry, dynamical systems, control theory, statistics and robotics. ***