Portrait von Kurt Gödel

Research of the key research area in logic, known as the "Kurt Gödel Research Center for Mathematical Logic", follows the tradition of Kurt Gödel, who proved his famous Completeness and Incompleteness Theorems in Vienna between 1929–1931, perhaps the most significant work of mathematical logic of modern times. His results were foundational for all the central areas of contemporary logic: set theory, model theory, computability theory, and proof theory. Current research in our key research area mainly focusses on set theory and model theory. Here, set theory offers both an axiomatic foundation for all mathematics as well as methods for the precise analysis of classification problems in mathematics (descriptive set theory). It traditionally has strong ties to analysis, ergodic theory, and topology. As the logical study of mathematical structures, model theory has found numerous applications in algebra, number theory, and analysis, and has seen a strong geometric orientation in the last few decades.