## Logic

**Set theory **and **model theory**, which are the principle areas of mathematical logic represented in Münster, concern themselves in different ways with fundamental questions of mathematics. The first studies natural models of set theory and the interplay between the existence of large cardinals, properties of definable sets of real numbers, combinatorial principles, and the cardinalities of specific sets. In model theory, one studies mathematical objects (groups, fields, geometries, ...) and examines their theories and the structure of their definable sets, considering properties such as stability. We analyse models of a theory, and use structural properties to better understand these models and to construct new examples.