LTG Logic and Theory Group

• Wednesday, 16-18
• Additional exercise lessons upon agreement

Lecture Room A97
Gebäude der Exakten Wissenschaften ("ExWi Building")
Sidlerstrasse 5

These lectures are about two foundamtal developments in mathematical logic: Gödel’s
incompleteness results and Gentzen’s approach to proof theory. Both had an enormous
impact on modern logic, computer science, and mathematics and had a crucial influence on
the following developments in these areas.

We start off from the foundational crisis in mathematics, Hilbert’s famous program as a
possible way to overcome this crisis, and Gödel’s results which show its limitations.
Both incompleteness theorems will be discussed in detail and put into the context of
other fundamental results concerning metamathematical questions.

Afterwards we turn to Gentzen’s approach to the consistency of Peano arithmetic PA which
is important for at least two reasons: (i) It provides a deeper understanding of the
consistency strength of PA and tells us a lot about the limitations of Hilbert’s program,
(ii) provides the basis for modern proof theory in mathematical logic and computer
science.

This lecture is well suited for students who are interested in logic and in the
foundations of mathematic and/or computer science. It provides an introduction into a
research topic which has been actively pursued in the Bern group during the previous
years.

Basic knowledge in mathematical logic and/or theoretical computer science.

To be announced.