After successful completion of the course, students are able to...

The intended result of this course is to understand the contents of the course. Among other effects, this understanding forms the basis for the capability to correctly reproduce the statements and notions covered in the course as well as for the ability to explain and apply the proof techniques used in the course.

Gödel's incompleteness theorems are among the most important results of
mathematical logic. In this lecture we will prove the incompleteness theorems.
In doing so we will not take the most direct route, instead we take the
incompleteness theorems as motivation to study topics and proof techniques in
their vicinity.

We start with a short introduction to computability theory which allows to get
to know the central proof techniques of diagonalisation and arithmetisation in
a comparatively simple setting. The consideration of the notion of truth in the
standard model will lead us to the logical level. Afterwards we will study
arithmetical theories and their non-standard models. Thus prepared we will
prove and discuss various forms and proofs of the incompleteness theorems.

Lecture

Oral exam

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Course notes will be made available.

Basic knowledge in mathematical logic as taught, e.g., in the courses VO + UE "Logic and Foundations of Mathematics".