GRK 806: Mathematical logic and applications

在过去的一个世纪里，数理逻辑已经从一门以基础为导向的科学发展成为一门数学学科，用新的思想、方法和结果丰富了传统的数学领域。与计算机科学的众多和不同的联系，部分源于数理逻辑，导致了这两个学科的相互进步。这个研究培训小组的重点是逻辑和计算机科学/数学之间的相互作用。特别强调的是逻辑方法的应用最近在计算机科学和代数中发挥核心作用的两个领域：模型检验：它将模型理论和有限结构中可计算性的研究与数据库理论、程序验证和基于约束的演绎中的问题结合起来。算术结构的模型理论：研究代数性质的可判断性问题及其与递归理论、模型理论和代数几何的相互作用。因此，研究培训小组处理从基本代数问题到信息技术应用的连贯的主题。研究计划的构建使参与的研究生和博士后在这些主题上发展出广泛的专业知识。

Over the past century, mathematical logic has developed from a foundationally oriented science to a mathematical discipline, enriching traditional areas of mathematics with new ideas, methods, and results. The numerous and diverse connections to computer science, whose origins lies in part in the mathematical logic, have led to the mutual advancement of both disciplines. This research training group focuses on the interplay between logic and computer science/mathematics. In particular the emphasis is on two areas where the application of logical methods has recently played a central role in computer science and algebra:Model checking: which combines model theory and the study of computability in finite structures with problems in database theory, program verification, and constraint-based deduction.Model theory of arithmetic structures: which examines decidability questions of an algebraic nature and their interplay with recursion theory, model theory, and algebraic geometry.The research training group addresses, therefore, a coherent subject matter ranging from fundamental algebraic questions to applications in the information technology.The studies program is constructed so that participating graduate students and postdoctoral fellows develop a broad expertise in these topics.