U.S.-Federal Republic of Germany Cooperative Research in Mathematical Logic

该奖项支持芝加哥大学的Robert Soare和Theodore Slaman以及耶鲁大学的Steffen Lempp对德意志联邦共和国进行几次短期研究访问，以便与海德堡大学的Klaus ambo - spies在数学逻辑的几个主题上进行合作。特别是，他们将继续研究递归函数理论和计算理论。芝加哥大学（Lempp最近在那里获得了博士学位）是这些主题的主要研究中心，这些美国数学家在该领域做出了一些杰出的贡献。德国在这一领域也有着悠久而杰出的传统，Ambos-Spies教授是德国递归函数理论的领军人物。他还在递归函数理论方法在计算复杂性方面的应用方面做了广泛的研究。Soare教授和Ambos-Spies教授之前的间歇性合作一直是相互激励和富有成效的。拟议的访问将使他们之间的合作更加频繁，并包括另外两位美国数学家，他们的工作与Ambos-Spies的工作直接相关。数理逻辑，特别是递归函数理论和计算理论最近在美国和国外非常活跃。递归理论起源于一种试图形式化一个集合是机械可定义的意思的尝试，因此它在理论计算机科学和计算复杂性理论中有应用。

This award supports several short term research visits to the Federal Republic of Germany by Robert Soare and Theodore Slaman of the University of Chicago and Steffen Lempp of Yale University in order to collaborate with Klaus Ambos-Spies of the University of Heidelberg in several topics of mathematical logic. In particular, they will pursue research on recursive function theory and the theory of computation. The University of Chicago (where Lempp recently obtained his PhD) is a major center of research on these topics and these U.S. mathematicians have produced some outstanding contributions to the field. Germany has a long and distinguished tradition in this field as well, and Professor Ambos-Spies is a leading figure in recursive function theory there. He has also done extensive research in applications of the methods of recursive function theory to computational complexity. Previous intermittent collaboration between Professors Soare and Ambos-Spies has been mutually stimulating and productive. The proposed visits will allow more frequent collaboration between them and the inclusion of two other U.S. mathematicians whose work is directly relevant to that of Ambos-Spies. Mathematical logic and particularly recursive function theory and the theory of computation have recently been very active in the U.S. and abroad. Recursion theory arises from an attempt to formalize what it means for a set to be mechanically definable, and thus it has applications to theoretical computer science and the theory of computational complexity.