Logic

Group Configuration
This diagram portrays the famous Group Configuration. In a stable structure, every such combinatorial configuration comes from a definable group.
© 2021

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.

Prerequisites

The courses on Mathematical Logic I and Mathematical Logic II with the following contents:

Methods of model construction, the Gödel completeness theorem, undecidability and the Gödel incompleteness theorems, axiomatic set theory, ordinals and cardinals.

Model theory has strong connections to algebra. Knowledge of algebra is therefore desirable for students who plan to specialise in model theory.

Courses for the Specialisation in "Logic"

Summer semester 2021

Prof. Dr. Ralf Schindler: Logic 4, Introduction to set theory, part 2 (Type II)
Prof. Dr. Dr. Katrin Tent: Introduction to Model Theory (Type I, II)

Winter semester 2021/2022

Prof. Dr. Aleksandra Kwiatkowska: "Logic 3: Topics in Descriptive Set Theory" (Type I, II)
Prof. Dr. Ralf Schindler: "Selected Topics from Set Theory" (Type II)
Prof. Dr. Dr. Katrin Tent: "Geometric Group Theory: Hyperbolic groups and small cancellation (Logic III)" (Type I, II)

Summer semester 2022

Prof. Dr. Martin Hils: "Model Theory: Introduction to NIP Theories" (Type I, II)
Prof. Dr. Dr. Katrin Tent: "Stable Groups" (Type I, II)

Winter semester 2022/2023

Dr. Martin Bays: "Logic 3 - Geometric Group Theory I" (Type I)
Prof. Dr. Ralf Schindler: "Logic 3 - Introduction to set theory" (Type I, II)

Summer semester 2023

Prof. Dr. Martin Hils: "Model Theory of Valued Fields" (Type I, II)
Prof. Dr. Ralf Schindler: "Selected Topics from Set Theory" (Type II)
 

Type I lecture courses may be taken as "Mathematical Logic 3", Type II as "Mathematical Logic 4".

Further information

The subject areas of the research groups are the following:

RG Set theory (Prof. Schindler)
RG Set theory (Prof. Schlutzenberg)
RG Descriptive set theory (Prof. Kwiatkowska)
RG Model theory and algebra (Prof. Hils)
RG Model theory and algebra (Prof. Jahnke)
RG Model theory and algebra (Prof. Tent)

Further information regarding lecture courses and student seminars which are offered in mathematical logic, as well as research seminars, master theses etc., can be found on the websites of these research groups.