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.

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.

This page presents the plan at the time of writing for the courses in future semesters. Please note that this plan is subject to change, and courses may be dropped, added, or modified in reaction to currently unforeseen events.

Courses for the Specialisation in "Logic"

Winter semester 2024/2025

Prof. Dr. Martin Hils: Model Theory of Pseudofinite Field (Type II)
Prof. Dr. Alexandra Kwiatkowska: Descriptive Set Theory (Type I, II)
Prof. Dr. Dr. Katrin Tent: Model Theory (Type I, II)

Summer semester 2024

Prof. Dr. Ralf Schindler: Logic 4: Selected Topics from Set Theory
Prof. Dr. Dr. Katrin Tent: Stable Groups

Winter semester 2023/2024

Prof. Dr. Aleksandra Kwiatkowska: "Logic 3: Abstract Topological Dynamics and Descriptive 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)

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)

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

Seminars

Winter semester 2024/2025

Prof. Dr. Martin Hils, Prof. Dr. Franziska Jahnke: Model Theory of the Witt-Frobenius
Prof. Dr. Ralf Schindler: Seminar on Set Theory

Further information

The subject areas of the research groups are the following:

RG Set theory (Prof. Schindler)
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.

Module representative

Prof. Dr. Martin Hils