GRK 806: Mathematical logic and applications

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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.