GRK 806: Mathematical logic and applications

在过去的世纪里，数理逻辑从一门基础科学发展成为一门数学学科，用新的思想、方法和成果丰富了数学的传统领域。计算机科学的起源部分在于数理逻辑，它与计算机科学的众多而多样的联系导致了这两个学科的共同进步。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。特别是重点是在两个领域的应用逻辑方法最近发挥了核心作用，在计算机科学和代数：模型检查：它结合了模型理论和研究的可计算性有限结构的问题，在数据库理论，程序验证，和基于约束的演绎。模型理论的算术结构：它考察了代数性质的可判定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，一个连贯的主题，从基本的代数问题到信息技术的应用。该研究计划的构建是为了使参与研究生和博士后研究员在这些主题中发展广泛的专业知识。

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.