Logic

Research with focus on 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, undeniably the most important work of mathematical Logic of the modern age. Gödel's results were fundamental to the central areas of modern logic: set theory, model theory, computability theory, and proof theory. Current research focuses  mainly on the areas of set theory and model theory. Set theory offers both an axiomatic foundation for all mathematics and 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 logic of mathematical structures, model theory has numerous, important applications in algebra, number theory and analysis, and has developed in the last few decades in a strongly geometrical manner.

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